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Model Misspecification and Linear Sandwiches

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Introduction

Traditional linear models, such as the output of the R function lm(), are often loaded with a set of strong assumptions. Take univariate regression:

\[ Y = q+mX+\varepsilon. (\#eq:lm) \] This equation assumes that:

  1. The conditional mean \(\mathbb E(Y\vert X) = q + mX\), a linear function of \(X\).
  2. The conditional variance \(\mathbb {V}(Y \vert X)=\mathbb{V}(\varepsilon\vert X)\) is independent of \(X\).
  3. The conditional distribution \(Y\vert X\) is gaussian.
  4. In a set of measurements \(\left\{\left(X_i,Y_i\right)\right\}_{i = 1,\, \dots, \,N}\), \(Y_i\) and the set \(\left\{ X_j, Y_j\right\} _{j\neq i}\) are conditionally independent of each other, given the value of the corresponding regressor \(X_i\).1

The last assumption is satisfied in many practical situations, and we will take it here for granted2. What happens when the first three assumptions are violated (that is “frequently” to “almost always”, depending on context)?

A comprehensive discussion is provided by (Buja et al. 2019). These authors show that:

Details can be found in the mentioned reference. The rest of the post illustrates with examples how to compute “sandwich” estimates in R, and why you may want to do so.

Fitting misspecified linear models in R

The {sandwich} package (available on CRAN) provides estimators for the regression coefficients’ variance-covariance matrix \(\mathbb V (\hat \beta)\) that are robust to first and second order misspecification. These can be readily used with lm objects, as in the example below:

fit <- lm(mpg ~ wt, data = mtcars)

stats::vcov(fit)  # standard vcov (linear model trusting estimate)
            (Intercept)        wt
(Intercept)    3.525484 -1.005693
wt            -1.005693  0.312594
sandwich::vcovHC(fit)  # sandwich vcov (model-robust estimate)
            (Intercept)         wt
(Intercept)    5.889249 -1.7418581
wt            -1.741858  0.5448011

It is important to note that both functions stats::vcov() and sandwich::vcovHC() employ the same point estimates of regression coefficients
to compute \(\mathbb V (\hat \beta)\):

fit

Call:
lm(formula = mpg ~ wt, data = mtcars)

Coefficients:
(Intercept)           wt  
     37.285       -5.344  

The difference between these functions lies in the different assumptions they make on the linear model residuals, which leads to different estimates for \(\mathbb{V}(\hat \beta)\).

Effects of misspecification

This section illustrates some consequences of model misspecification through simulation. The examples use:

library(dplyr)
library(ggplot2)

For convenience, we define some helpers to be used in the following examples. The function below returns random generators for the generic additive error model \(Y = f(X) + \varepsilon\), where the distribution of the noise term \(\varepsilon\) may in general depend on \(X\). Both \(X\) and \(Y\) are assumed here and below to be 1-dimensional.

rxy_fun <- function(rx, f, reps) {
    res <- function(n) {
        x <- rx(n)  # X has marginal distribution 'rx'
        y <- f(x) + reps(x)  # Y has conditional mean 'f(x)' and noise 'reps(x)'
        return(tibble(x = x, y = y))  
    }
    return(structure(res, class = "rxy"))
}

plot.rxy <- function(x, N = 1000, seed = 840) {
    set.seed(seed)
    
    ggplot(data = x(N), aes(x = x, y = y)) +
        geom_point(alpha = 0.3) + 
        geom_smooth(method = "lm", se = FALSE)
}

The following function simulates fitting the linear model y ~ x over multiple datasets generated according to a function rxy().

lmsim <- function(rxy, N = 100, vcov = stats::vcov, B = 1e3, seed = 840) 
{ 
    set.seed(seed)
    
    res <- list(coef = matrix(nrow = B, ncol = 2), vcov = vector("list", B))
    colnames(res$coef) <- c("(Intercept)", "x")
    class(res) <- "lmsim"
                                
    for (b in 1:B) {
        .fit <- lm(y ~ ., data = rxy(N))
        res$coef[b, ] <- coef(.fit)  # Store intercept and slope in B x 2 matrix
        res$vcov[[b]] <- vcov(.fit)  # Store vcov estimates in length B list. 
    }
    
    return(res)
}

print.lmsim <- function(x) 
{
    cat("Simulation results:\n\n")
    cat("* Model-trusting vcov (average of vcov estimates):\n")
    print( avg_est_vcov <- Reduce("+", x$vcov) / length(x$vcov) )
    cat("\n* Simulation-based vcov (vcov of coefficient estimates):\n")
    print( emp_vcov <- cov(x$coef))
    cat("\n* Ratio (1st / 2nd):\n")
    print( avg_est_vcov / emp_vcov )
    return(invisible(x))
}

The print method defined above shows a comparison of the covariance matrices obtained by:

  1. Averaging variance-covariance estimates from the various simulations, and
  2. Taking the variance-covariance matrix of regression coefficients obtained in the simulations.

The first one can be considered a “model-trusting” estimate (where the actual “model” is specified by the vcov argument of lmsim(), i.e. stats::vcov and sandwich::vcovHC for the traditional and sandwich estimates, respectively). The second one is a model-free simulation-based estimate of the true \(\mathbb{V}(\hat \beta)\). The comparison between the two4 provides a measure of the asymptotic bias of the model-trusting estimate.

Example 1: First order misspecification

\[ Y = X ^ 2 + \varepsilon,\quad X \sim \text{Unif} (0,1),\qquad \varepsilon \sim \mathcal N (0,0.01) \]

rxy_01 <- rxy_fun(
    rx = runif,
    f = \(x) x^2,
    reps = \(x) rnorm(length(x), sd = .01)
    )

In this model, \(\mathbb E (Y \vert X)\) is not linear in \(X\) (first order misspecification), but the remaining assumptions of the linear model hold. This is how a typical linear fit of data generated from this model looks like:

plot(rxy_01, N = 300)

Here the effect of misspecification on the variance-covariance model trusting estimates is to underestimate true covariance values (by a factor as large as 40%!):

lmsim(rxy_01)
$coef
        (Intercept)         x
   [1,]  -0.1492042 0.9848331
   [2,]  -0.1672965 0.9938356
   [3,]  -0.1741689 1.0133387
   [4,]  -0.1343376 0.9338718
   [5,]  -0.1522985 0.9771531
   [6,]  -0.1617622 0.9735575
   [7,]  -0.1850168 1.0479047
   [8,]  -0.1725564 1.0150846
   [9,]  -0.1519079 0.9797259
  [10,]  -0.1701713 1.0003935
  [11,]  -0.1776876 1.0118800
  [12,]  -0.1726425 0.9886916
  [13,]  -0.1530396 0.9900055
  [14,]  -0.1730381 1.0118988
  [15,]  -0.1552507 0.9641413
  [16,]  -0.1820366 1.0249481
  [17,]  -0.1379366 0.9518739
  [18,]  -0.1804744 1.0215438
  [19,]  -0.1596881 0.9879221
  [20,]  -0.1551352 0.9623821
  [21,]  -0.1487741 0.9924152
  [22,]  -0.1818460 1.0203085
  [23,]  -0.1390505 0.9452565
  [24,]  -0.1709407 1.0155853
  [25,]  -0.1615616 0.9701107
  [26,]  -0.1732873 1.0139951
  [27,]  -0.1584225 0.9845009
  [28,]  -0.1734871 0.9899266
  [29,]  -0.1499159 0.9979010
  [30,]  -0.1640850 1.0128128
  [31,]  -0.1584035 0.9897784
  [32,]  -0.1597918 0.9626873
  [33,]  -0.1713458 0.9876645
  [34,]  -0.1720940 1.0101869
  [35,]  -0.1561971 0.9963491
  [36,]  -0.1598678 0.9880583
  [37,]  -0.1959328 1.0326375
  [38,]  -0.1707688 0.9805662
  [39,]  -0.1730277 1.0205506
  [40,]  -0.1546160 0.9629526
  [41,]  -0.1609785 1.0096706
  [42,]  -0.1430278 0.9791670
  [43,]  -0.1481606 0.9704052
  [44,]  -0.1812934 1.0069203
  [45,]  -0.1624797 0.9954147
  [46,]  -0.2263972 1.1074251
  [47,]  -0.1460128 0.9668403
  [48,]  -0.1727529 0.9936889
  [49,]  -0.1551878 0.9793975
  [50,]  -0.1704082 0.9901274
  [51,]  -0.1322900 0.9406920
  [52,]  -0.1494835 1.0049753
  [53,]  -0.1631515 1.0072997
  [54,]  -0.1538023 0.9660115
  [55,]  -0.1730536 1.0106522
  [56,]  -0.1715305 1.0217686
  [57,]  -0.1738781 1.0340199
  [58,]  -0.1724760 1.0008378
  [59,]  -0.1393797 0.9725650
  [60,]  -0.1797192 1.0191456
  [61,]  -0.1609190 0.9752423
  [62,]  -0.1756820 1.0313139
  [63,]  -0.2147338 1.0747649
  [64,]  -0.1700265 1.0148409
  [65,]  -0.1890362 1.0486265
  [66,]  -0.1830241 1.0085895
  [67,]  -0.1742902 1.0161591
  [68,]  -0.1240727 0.8975975
  [69,]  -0.1510721 0.9566539
  [70,]  -0.1506778 0.9852273
  [71,]  -0.1697857 1.0207411
  [72,]  -0.1592230 1.0033666
  [73,]  -0.1783334 1.0296205
  [74,]  -0.1545865 0.9922272
  [75,]  -0.1592670 0.9836079
  [76,]  -0.1492947 0.9775454
  [77,]  -0.1817262 1.0356666
  [78,]  -0.1405081 0.9463266
  [79,]  -0.1802573 1.0244577
  [80,]  -0.2008736 1.0651887
  [81,]  -0.1444640 0.9915624
  [82,]  -0.2157661 1.0890302
  [83,]  -0.1969575 1.0552697
  [84,]  -0.1751485 1.0199630
  [85,]  -0.1739127 0.9967420
  [86,]  -0.1419502 0.9484813
  [87,]  -0.1914078 1.0264140
  [88,]  -0.1745678 0.9988856
  [89,]  -0.1574870 0.9861215
  [90,]  -0.1776541 1.0421064
  [91,]  -0.1650321 0.9969632
  [92,]  -0.1805436 1.0251750
  [93,]  -0.1774267 0.9925020
  [94,]  -0.1684783 1.0034823
  [95,]  -0.1622454 0.9629651
  [96,]  -0.1583735 0.9747504
  [97,]  -0.1475453 0.9814714
  [98,]  -0.1631432 0.9853327
  [99,]  -0.1974697 1.0387027
 [100,]  -0.1506777 0.9935551
 [101,]  -0.1973696 1.0532105
 [102,]  -0.1854300 1.0202853
 [103,]  -0.1743934 1.0070743
 [104,]  -0.1907374 1.0259785
 [105,]  -0.2079500 1.0360323
 [106,]  -0.1643661 1.0091753
 [107,]  -0.2026129 1.0608377
 [108,]  -0.1839888 1.0241692
 [109,]  -0.1700652 1.0326750
 [110,]  -0.1778231 1.0074247
 [111,]  -0.1634512 1.0011191
 [112,]  -0.1633072 1.0092457
 [113,]  -0.1804383 1.0267848
 [114,]  -0.1573277 1.0066673
 [115,]  -0.1345778 0.9275003
 [116,]  -0.1950365 1.0409511
 [117,]  -0.1761704 1.0138517
 [118,]  -0.1529808 0.9970803
 [119,]  -0.1386321 0.9238803
 [120,]  -0.1541518 0.9836478
 [121,]  -0.1775055 1.0246489
 [122,]  -0.1922580 1.0568006
 [123,]  -0.1779449 0.9919571
 [124,]  -0.1845176 1.0219276
 [125,]  -0.2156581 1.0853025
 [126,]  -0.1491147 0.9495424
 [127,]  -0.1551748 0.9757274
 [128,]  -0.1892170 1.0467927
 [129,]  -0.1430404 0.9542750
 [130,]  -0.1580013 0.9779809
 [131,]  -0.1438539 0.9703157
 [132,]  -0.1692766 1.0189915
 [133,]  -0.1693396 1.0114952
 [134,]  -0.1798591 1.0212778
 [135,]  -0.1964096 1.0509122
 [136,]  -0.1728542 1.0378895
 [137,]  -0.2090140 1.0760444
 [138,]  -0.1570607 1.0068291
 [139,]  -0.1733614 0.9977447
 [140,]  -0.1696596 0.9795989
 [141,]  -0.1580316 0.9790548
 [142,]  -0.1799208 1.0134743
 [143,]  -0.1445422 0.9518618
 [144,]  -0.1649267 0.9938346
 [145,]  -0.1725723 1.0238495
 [146,]  -0.1599091 0.9665131
 [147,]  -0.1923726 1.0330380
 [148,]  -0.1973959 1.0584268
 [149,]  -0.1463507 0.9644216
 [150,]  -0.1679247 1.0089701
 [151,]  -0.1750804 1.0313828
 [152,]  -0.1957230 1.0514504
 [153,]  -0.1673706 1.0119983
 [154,]  -0.1682516 1.0134721
 [155,]  -0.1671656 1.0050093
 [156,]  -0.1485667 0.9525622
 [157,]  -0.2018525 1.0410615
 [158,]  -0.2128565 1.0654944
 [159,]  -0.1935343 1.0306762
 [160,]  -0.1367284 0.9428695
 [161,]  -0.1406401 0.9776211
 [162,]  -0.1925020 1.0358385
 [163,]  -0.1666279 0.9908879
 [164,]  -0.1813802 1.0133285
 [165,]  -0.1500137 0.9724187
 [166,]  -0.1298679 0.9225217
 [167,]  -0.1830164 1.0301854
 [168,]  -0.1361425 0.9660179
 [169,]  -0.1786530 1.0037611
 [170,]  -0.1763439 1.0056544
 [171,]  -0.1847810 1.0225125
 [172,]  -0.1633224 0.9790834
 [173,]  -0.1632595 1.0048817
 [174,]  -0.1521565 0.9691901
 [175,]  -0.1501240 0.9641523
 [176,]  -0.1852384 1.0315249
 [177,]  -0.1447913 0.9302012
 [178,]  -0.1876313 1.0383718
 [179,]  -0.1658932 0.9864247
 [180,]  -0.1329441 0.9498161
 [181,]  -0.1747157 1.0154394
 [182,]  -0.1719564 1.0062216
 [183,]  -0.1721170 0.9974692
 [184,]  -0.1677693 1.0176596
 [185,]  -0.1698480 1.0130385
 [186,]  -0.2131021 1.1038004
 [187,]  -0.1520521 0.9524128
 [188,]  -0.2064924 1.0603008
 [189,]  -0.1682670 0.9910281
 [190,]  -0.1705248 1.0121078
 [191,]  -0.1545912 0.9830719
 [192,]  -0.1659990 0.9808501
 [193,]  -0.1653286 1.0106849
 [194,]  -0.1564038 0.9819012
 [195,]  -0.1576622 0.9910821
 [196,]  -0.1663288 1.0007883
 [197,]  -0.1251622 0.9413586
 [198,]  -0.1749056 1.0259633
 [199,]  -0.1726707 1.0073847
 [200,]  -0.1743689 1.0287916
 [201,]  -0.1763904 1.0105388
 [202,]  -0.1485123 1.0033058
 [203,]  -0.2117403 1.0559125
 [204,]  -0.1680369 1.0022455
 [205,]  -0.1844290 1.0293421
 [206,]  -0.1733969 1.0131757
 [207,]  -0.1232361 0.9085716
 [208,]  -0.1835077 0.9984445
 [209,]  -0.1801353 1.0461562
 [210,]  -0.1874809 1.0410110
 [211,]  -0.1512918 0.9598340
 [212,]  -0.1717485 1.0119172
 [213,]  -0.1693144 1.0184664
 [214,]  -0.1576858 0.9814377
 [215,]  -0.1555694 0.9852405
 [216,]  -0.1720713 0.9953904
 [217,]  -0.1549881 0.9673649
 [218,]  -0.1771679 1.0256871
 [219,]  -0.1211022 0.9105356
 [220,]  -0.1303083 0.9353758
 [221,]  -0.1632698 1.0045698
 [222,]  -0.1463544 0.9706859
 [223,]  -0.1446694 0.9729244
 [224,]  -0.1507870 0.9649947
 [225,]  -0.1860260 1.0327242
 [226,]  -0.1714667 1.0052976
 [227,]  -0.1607564 0.9804749
 [228,]  -0.1787528 1.0006837
 [229,]  -0.1565934 0.9884775
 [230,]  -0.1570377 0.9678156
 [231,]  -0.1596805 1.0008489
 [232,]  -0.1663957 1.0274998
 [233,]  -0.1454704 0.9364282
 [234,]  -0.1803635 1.0212843
 [235,]  -0.1781276 1.0155589
 [236,]  -0.1786070 1.0281397
 [237,]  -0.1460048 0.9497290
 [238,]  -0.1627864 0.9700011
 [239,]  -0.1625018 0.9903388
 [240,]  -0.1724135 0.9858393
 [241,]  -0.1884628 1.0240039
 [242,]  -0.1392754 0.9426642
 [243,]  -0.1910326 1.0432209
 [244,]  -0.1653891 0.9642670
 [245,]  -0.1766557 1.0069076
 [246,]  -0.1396503 0.9443030
 [247,]  -0.1747318 1.0180222
 [248,]  -0.1629340 0.9904048
 [249,]  -0.1586271 0.9946838
 [250,]  -0.1374020 0.9343580
 [251,]  -0.1337354 0.9228731
 [252,]  -0.1720418 1.0191555
 [253,]  -0.1607660 1.0019473
 [254,]  -0.1470943 0.9869176
 [255,]  -0.2036385 1.0454900
 [256,]  -0.1462811 0.9548304
 [257,]  -0.1741273 1.0304742
 [258,]  -0.1212441 0.9203724
 [259,]  -0.1646721 0.9912321
 [260,]  -0.2193445 1.0931664
 [261,]  -0.1680506 1.0227414
 [262,]  -0.1726858 1.0149215
 [263,]  -0.1964757 1.0567797
 [264,]  -0.1370500 0.9263424
 [265,]  -0.1604476 0.9962605
 [266,]  -0.1697485 1.0204291
 [267,]  -0.1757017 1.0036071
 [268,]  -0.1505578 0.9588509
 [269,]  -0.1776712 1.0317416
 [270,]  -0.1936083 1.0560750
 [271,]  -0.1662493 0.9846882
 [272,]  -0.1608127 0.9574892
 [273,]  -0.1557933 0.9761793
 [274,]  -0.1529221 0.9815921
 [275,]  -0.1717047 0.9917627
 [276,]  -0.1696310 0.9890217
 [277,]  -0.1680761 0.9969446
 [278,]  -0.1610546 0.9719813
 [279,]  -0.2044580 1.0539898
 [280,]  -0.1578984 0.9772140
 [281,]  -0.1583088 0.9931033
 [282,]  -0.1992136 1.0471801
 [283,]  -0.1874156 1.0328504
 [284,]  -0.1398905 0.9204460
 [285,]  -0.1753104 0.9916116
 [286,]  -0.1343638 0.9326845
 [287,]  -0.1538998 1.0060365
 [288,]  -0.1760144 1.0207676
 [289,]  -0.1388620 0.9637450
 [290,]  -0.1816857 1.0328560
 [291,]  -0.1687266 1.0156244
 [292,]  -0.1766941 1.0460703
 [293,]  -0.1527780 0.9473203
 [294,]  -0.1658256 0.9693212
 [295,]  -0.1622672 1.0045611
 [296,]  -0.1426372 0.9485901
 [297,]  -0.1674830 1.0046266
 [298,]  -0.1790086 1.0198079
 [299,]  -0.1397103 0.9316240
 [300,]  -0.1410791 0.9538880
 [301,]  -0.1520688 0.9678901
 [302,]  -0.1899214 1.0290082
 [303,]  -0.1504792 0.9637337
 [304,]  -0.1643493 1.0011869
 [305,]  -0.1331099 0.9419335
 [306,]  -0.1563723 0.9764814
 [307,]  -0.1628858 1.0001923
 [308,]  -0.1667569 0.9915934
 [309,]  -0.1529791 0.9741474
 [310,]  -0.1640690 1.0023149
 [311,]  -0.1972968 1.0506719
 [312,]  -0.2055455 1.0644095
 [313,]  -0.1472489 0.9832079
 [314,]  -0.1749494 1.0105527
 [315,]  -0.1460915 0.9906040
 [316,]  -0.1796034 1.0252346
 [317,]  -0.1863635 1.0323918
 [318,]  -0.2013777 1.0461774
 [319,]  -0.1608490 0.9924077
 [320,]  -0.1871862 1.0209730
 [321,]  -0.1799796 1.0290107
 [322,]  -0.1616459 0.9746576
 [323,]  -0.1365747 0.9443577
 [324,]  -0.1481246 0.9841136
 [325,]  -0.1764505 1.0284868
 [326,]  -0.2124155 1.0843911
 [327,]  -0.1631815 1.0070212
 [328,]  -0.1674173 0.9951164
 [329,]  -0.1839151 1.0392863
 [330,]  -0.1775244 0.9911864
 [331,]  -0.1534663 0.9559287
 [332,]  -0.1761140 1.0194389
 [333,]  -0.1493893 0.9898809
 [334,]  -0.1400167 0.9638405
 [335,]  -0.1544377 0.9882799
 [336,]  -0.1735703 1.0059490
 [337,]  -0.1626174 1.0025301
 [338,]  -0.1581419 0.9861419
 [339,]  -0.1730115 1.0124530
 [340,]  -0.1563788 0.9949382
 [341,]  -0.1752076 1.0172927
 [342,]  -0.1456022 0.9772894
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 [793,]  -0.2055792 1.0642680
 [794,]  -0.1607430 0.9879502
 [795,]  -0.1485527 0.9707901
 [796,]  -0.1869104 1.0448167
 [797,]  -0.1432264 0.9497442
 [798,]  -0.1551319 0.9866224
 [799,]  -0.1616155 1.0065054
 [800,]  -0.1644768 1.0067670
 [801,]  -0.1636772 1.0026145
 [802,]  -0.1869406 1.0469519
 [803,]  -0.1631803 0.9832520
 [804,]  -0.1335775 0.9057236
 [805,]  -0.1886888 1.0262489
 [806,]  -0.1740655 1.0156793
 [807,]  -0.1561986 0.9820559
 [808,]  -0.2037931 1.0512346
 [809,]  -0.1741981 1.0344614
 [810,]  -0.1829535 1.0105330
 [811,]  -0.1896020 1.0421828
 [812,]  -0.1662236 1.0043542
 [813,]  -0.1792341 0.9928661
 [814,]  -0.1521315 0.9529703
 [815,]  -0.1440783 0.9701183
 [816,]  -0.1622361 0.9981414
 [817,]  -0.1805512 1.0191505
 [818,]  -0.1607819 0.9624290
 [819,]  -0.1420713 0.9380359
 [820,]  -0.1643421 1.0151680
 [821,]  -0.1664652 1.0137762
 [822,]  -0.1371331 0.9379677
 [823,]  -0.1866094 1.0364502
 [824,]  -0.1528968 0.9915065
 [825,]  -0.1616655 0.9835068
 [826,]  -0.1854498 1.0233392
 [827,]  -0.1696280 1.0055116
 [828,]  -0.1612802 0.9875495
 [829,]  -0.1544984 1.0139563
 [830,]  -0.1658774 1.0025752
 [831,]  -0.1642900 0.9978620
 [832,]  -0.1724980 1.0460019
 [833,]  -0.1452499 0.9690060
 [834,]  -0.1912204 1.0254658
 [835,]  -0.1800559 1.0091060
 [836,]  -0.1778441 1.0300128
 [837,]  -0.1811142 1.0332075
 [838,]  -0.1624216 0.9931996
 [839,]  -0.1731638 0.9761660
 [840,]  -0.1602737 0.9564707
 [841,]  -0.1753463 1.0081394
 [842,]  -0.1406723 0.9695324
 [843,]  -0.1789439 1.0020023
 [844,]  -0.1630913 0.9970695
 [845,]  -0.1752290 0.9999347
 [846,]  -0.1622860 0.9890234
 [847,]  -0.1842694 1.0110108
 [848,]  -0.1720268 0.9939975
 [849,]  -0.1738113 1.0088941
 [850,]  -0.2054332 1.0772987
 [851,]  -0.1732703 1.0133332
 [852,]  -0.1848207 1.0306298
 [853,]  -0.1688346 1.0205498
 [854,]  -0.1505759 0.9703343
 [855,]  -0.1735229 1.0295333
 [856,]  -0.1869735 1.0433806
 [857,]  -0.1764856 1.0062419
 [858,]  -0.1536178 1.0033897
 [859,]  -0.1718611 0.9955814
 [860,]  -0.1348844 0.9437839
 [861,]  -0.1892973 1.0193578
 [862,]  -0.1882183 1.0286911
 [863,]  -0.1715716 1.0047731
 [864,]  -0.1806253 1.0267766
 [865,]  -0.1694987 0.9915604
 [866,]  -0.1516368 0.9541116
 [867,]  -0.1750902 1.0185156
 [868,]  -0.1675485 1.0070588
 [869,]  -0.1386680 0.9501183
 [870,]  -0.1756657 1.0235620
 [871,]  -0.1666412 1.0029049
 [872,]  -0.1611926 1.0265492
 [873,]  -0.1634887 0.9804824
 [874,]  -0.1728598 1.0163720
 [875,]  -0.1161671 0.8971733
 [876,]  -0.1672444 0.9952969
 [877,]  -0.1719615 1.0070991
 [878,]  -0.1591452 1.0120340
 [879,]  -0.1352738 0.9641847
 [880,]  -0.1961992 1.0380459
 [881,]  -0.1721523 1.0142950
 [882,]  -0.1692813 1.0252897
 [883,]  -0.2005558 1.0516790
 [884,]  -0.1582444 0.9565389
 [885,]  -0.1908112 1.0369241
 [886,]  -0.1556667 0.9936260
 [887,]  -0.1470472 0.9454042
 [888,]  -0.2047328 1.0507258
 [889,]  -0.1515883 0.9789401
 [890,]  -0.1622987 0.9880549
 [891,]  -0.1600290 1.0129990
 [892,]  -0.1532964 0.9740795
 [893,]  -0.1667343 0.9814003
 [894,]  -0.1743407 1.0059649
 [895,]  -0.1597287 1.0041655
 [896,]  -0.1598353 0.9577908
 [897,]  -0.1747722 1.0166803
 [898,]  -0.1719665 1.0172177
 [899,]  -0.1894487 1.0339012
 [900,]  -0.1760002 1.0206094
 [901,]  -0.1765603 1.0003902
 [902,]  -0.1658552 1.0151482
 [903,]  -0.1500426 0.9729887
 [904,]  -0.1674547 1.0207010
 [905,]  -0.1760547 1.0151896
 [906,]  -0.1523639 0.9793935
 [907,]  -0.1750210 1.0191295
 [908,]  -0.1653355 1.0006676
 [909,]  -0.1786037 1.0285421
 [910,]  -0.1435760 0.9549144
 [911,]  -0.1658090 0.9870342
 [912,]  -0.1916508 1.0380478
 [913,]  -0.1565003 0.9805763
 [914,]  -0.1763433 1.0286954
 [915,]  -0.2367715 1.0984673
 [916,]  -0.1982123 1.0457465
 [917,]  -0.1697756 1.0029979
 [918,]  -0.1836452 1.0334605
 [919,]  -0.1726370 1.0330784
 [920,]  -0.1683219 1.0121307
 [921,]  -0.1796113 1.0171441
 [922,]  -0.1809396 1.0491079
 [923,]  -0.1945712 1.0215810
 [924,]  -0.1506410 0.9826792
 [925,]  -0.1800323 1.0367853
 [926,]  -0.1646551 1.0000640
 [927,]  -0.1559406 0.9898952
 [928,]  -0.1659323 1.0084276
 [929,]  -0.1593027 0.9883255
 [930,]  -0.1611286 0.9848828
 [931,]  -0.1484368 0.9611656
 [932,]  -0.1907006 1.0490519
 [933,]  -0.1735598 0.9850736
 [934,]  -0.1532961 0.9565456
 [935,]  -0.1874186 1.0352017
 [936,]  -0.1784458 1.0178469
 [937,]  -0.1751489 1.0095368
 [938,]  -0.1433234 0.9663845
 [939,]  -0.2081658 1.0826374
 [940,]  -0.1976953 1.0388597
 [941,]  -0.2006691 1.0424814
 [942,]  -0.1713905 0.9848923
 [943,]  -0.1579937 0.9845753
 [944,]  -0.1590341 0.9805592
 [945,]  -0.1624735 0.9972820
 [946,]  -0.1548385 0.9607173
 [947,]  -0.1490660 0.9653262
 [948,]  -0.1989202 1.0552705
 [949,]  -0.1568205 0.9723116
 [950,]  -0.1759609 1.0113120
 [951,]  -0.1549532 1.0071352
 [952,]  -0.1699052 1.0203925
 [953,]  -0.1299368 0.9368096
 [954,]  -0.1606578 0.9957644
 [955,]  -0.1700132 0.9745825
 [956,]  -0.1474418 0.9532069
 [957,]  -0.1648604 0.9976720
 [958,]  -0.1561832 0.9625276
 [959,]  -0.1692921 1.0117697
 [960,]  -0.1860920 1.0244146
 [961,]  -0.1843421 1.0329883
 [962,]  -0.1515894 0.9918073
 [963,]  -0.1714614 1.0269564
 [964,]  -0.1610199 1.0032958
 [965,]  -0.1682890 1.0271230
 [966,]  -0.1644756 1.0035257
 [967,]  -0.1600014 0.9744283
 [968,]  -0.2012037 1.0664731
 [969,]  -0.1527193 0.9848182
 [970,]  -0.1678397 0.9946171
 [971,]  -0.1437448 0.9350025
 [972,]  -0.1550885 0.9646264
 [973,]  -0.1694720 0.9833348
 [974,]  -0.1722868 1.0134666
 [975,]  -0.1311282 0.9359723
 [976,]  -0.1710689 0.9888027
 [977,]  -0.1860245 1.0053996
 [978,]  -0.1520098 0.9745218
 [979,]  -0.1393123 0.9583837
 [980,]  -0.1550963 0.9735025
 [981,]  -0.1686412 1.0256554
 [982,]  -0.1683808 1.0051600
 [983,]  -0.2038087 1.0597734
 [984,]  -0.1556640 0.9724131
 [985,]  -0.1518065 0.9794142
 [986,]  -0.1318841 0.9790193
 [987,]  -0.1602138 1.0004644
 [988,]  -0.1816916 1.0370025
 [989,]  -0.1794502 1.0468634
 [990,]  -0.1637645 0.9923290
 [991,]  -0.1704909 0.9907060
 [992,]  -0.1313033 0.9166676
 [993,]  -0.1597615 0.9924357
 [994,]  -0.1855906 1.0558936
 [995,]  -0.1635394 1.0259573
 [996,]  -0.1654512 0.9871150
 [997,]  -0.1473220 0.9665995
 [998,]  -0.1629013 1.0051578
 [999,]  -0.1484551 0.9735056
[1000,]  -0.1589381 0.9996720

$vcov
$vcov[[1]]
              (Intercept)             x
(Intercept)  0.0002450162 -0.0003571999
x           -0.0003571999  0.0007101622

$vcov[[2]]
              (Intercept)             x
(Intercept)  0.0002101647 -0.0003215567
x           -0.0003215567  0.0006591549

$vcov[[3]]
              (Intercept)             x
(Intercept)  0.0002179332 -0.0003286406
x           -0.0003286406  0.0006650377

$vcov[[4]]
              (Intercept)             x
(Intercept)  0.0002243474 -0.0003426187
x           -0.0003426187  0.0007126448

$vcov[[5]]
              (Intercept)             x
(Intercept)  0.0002424802 -0.0003616203
x           -0.0003616203  0.0007216100

$vcov[[6]]
              (Intercept)             x
(Intercept)  0.0002018983 -0.0003285588
x           -0.0003285588  0.0007254109

$vcov[[7]]
              (Intercept)             x
(Intercept)  0.0002418026 -0.0003476748
x           -0.0003476748  0.0006596267

$vcov[[8]]
              (Intercept)             x
(Intercept)  0.0002539583 -0.0003714388
x           -0.0003714388  0.0007134345

$vcov[[9]]
             (Intercept)             x
(Intercept)  0.000236378 -0.0003467000
x           -0.000346700  0.0006871777

$vcov[[10]]
              (Intercept)             x
(Intercept)  0.0002281523 -0.0003493466
x           -0.0003493466  0.0007117159

$vcov[[11]]
              (Intercept)             x
(Intercept)  0.0001860037 -0.0002866660
x           -0.0002866660  0.0005870313

$vcov[[12]]
              (Intercept)             x
(Intercept)  0.0001934365 -0.0003160700
x           -0.0003160700  0.0006875627

$vcov[[13]]
              (Intercept)             x
(Intercept)  0.0002374079 -0.0003455608
x           -0.0003455608  0.0006967372

$vcov[[14]]
              (Intercept)             x
(Intercept)  0.0001993149 -0.0003017607
x           -0.0003017607  0.0006219343

$vcov[[15]]
              (Intercept)             x
(Intercept)  0.0002088154 -0.0003303078
x           -0.0003303078  0.0007030159

$vcov[[16]]
              (Intercept)             x
(Intercept)  0.0001985756 -0.0003047744
x           -0.0003047744  0.0006298834

$vcov[[17]]
              (Intercept)             x
(Intercept)  0.0001786153 -0.0002802310
x           -0.0002802310  0.0006402416

$vcov[[18]]
              (Intercept)             x
(Intercept)  0.0001911901 -0.0002959856
x           -0.0002959856  0.0006142449

$vcov[[19]]
              (Intercept)             x
(Intercept)  0.0002123219 -0.0003271442
x           -0.0003271442  0.0006854389

$vcov[[20]]
              (Intercept)             x
(Intercept)  0.0001978822 -0.0003179431
x           -0.0003179431  0.0006909555

$vcov[[21]]
              (Intercept)             x
(Intercept)  0.0002382875 -0.0003540322
x           -0.0003540322  0.0007567870

$vcov[[22]]
              (Intercept)             x
(Intercept)  0.0002573581 -0.0003869010
x           -0.0003869010  0.0007538442

$vcov[[23]]
              (Intercept)             x
(Intercept)  0.0001808243 -0.0002899308
x           -0.0002899308  0.0006639026

$vcov[[24]]
              (Intercept)             x
(Intercept)  0.0002280476 -0.0003344769
x           -0.0003344769  0.0006520818

$vcov[[25]]
              (Intercept)             x
(Intercept)  0.0001923447 -0.0003103562
x           -0.0003103562  0.0006683000

$vcov[[26]]
              (Intercept)             x
(Intercept)  0.0002503819 -0.0003698259
x           -0.0003698259  0.0007203578

$vcov[[27]]
              (Intercept)             x
(Intercept)  0.0002131530 -0.0003224128
x           -0.0003224128  0.0006617047

$vcov[[28]]
              (Intercept)             x
(Intercept)  0.0001758063 -0.0002865502
x           -0.0002865502  0.0006190637

$vcov[[29]]
              (Intercept)             x
(Intercept)  0.0002368937 -0.0003380764
x           -0.0003380764  0.0006633968

$vcov[[30]]
              (Intercept)             x
(Intercept)  0.0002359442 -0.0003479580
x           -0.0003479580  0.0007011781

$vcov[[31]]
              (Intercept)             x
(Intercept)  0.0002225926 -0.0003473768
x           -0.0003473768  0.0007579507

$vcov[[32]]
              (Intercept)             x
(Intercept)  0.0002014779 -0.0003033437
x           -0.0003033437  0.0005656145

$vcov[[33]]
              (Intercept)             x
(Intercept)  0.0002259112 -0.0003459837
x           -0.0003459837  0.0006804181

$vcov[[34]]
              (Intercept)             x
(Intercept)  0.0002007661 -0.0003037831
x           -0.0003037831  0.0006177833

$vcov[[35]]
              (Intercept)             x
(Intercept)  0.0002399043 -0.0003434288
x           -0.0003434288  0.0006616459

$vcov[[36]]
              (Intercept)             x
(Intercept)  0.0002257102 -0.0003377113
x           -0.0003377113  0.0006720374

$vcov[[37]]
              (Intercept)             x
(Intercept)  0.0002493569 -0.0003866623
x           -0.0003866623  0.0007669480

$vcov[[38]]
              (Intercept)             x
(Intercept)  0.0002575960 -0.0003989763
x           -0.0003989763  0.0007887240

$vcov[[39]]
              (Intercept)             x
(Intercept)  0.0002171891 -0.0003219332
x           -0.0003219332  0.0006561724

$vcov[[40]]
              (Intercept)             x
(Intercept)  0.0002361582 -0.0003686105
x           -0.0003686105  0.0007621286

$vcov[[41]]
              (Intercept)             x
(Intercept)  0.0002308098 -0.0003412070
x           -0.0003412070  0.0007019272

$vcov[[42]]
              (Intercept)             x
(Intercept)  0.0002314122 -0.0003244172
x           -0.0003244172  0.0005983842

$vcov[[43]]
              (Intercept)             x
(Intercept)  0.0002205026 -0.0003343660
x           -0.0003343660  0.0007098778

$vcov[[44]]
              (Intercept)             x
(Intercept)  0.0002146571 -0.0003312574
x           -0.0003312574  0.0006543200

$vcov[[45]]
              (Intercept)             x
(Intercept)  0.0002226960 -0.0003324958
x           -0.0003324958  0.0006618336

$vcov[[46]]
              (Intercept)             x
(Intercept)  0.0002981846 -0.0004091152
x           -0.0004091152  0.0006849014

$vcov[[47]]
              (Intercept)             x
(Intercept)  0.0002483760 -0.0003613474
x           -0.0003613474  0.0006912999

$vcov[[48]]
              (Intercept)             x
(Intercept)  0.0002381058 -0.0003597257
x           -0.0003597257  0.0006968654

$vcov[[49]]
              (Intercept)             x
(Intercept)  0.0002052974 -0.0003199494
x           -0.0003199494  0.0006912629

$vcov[[50]]
              (Intercept)             x
(Intercept)  0.0002125383 -0.0003427123
x           -0.0003427123  0.0007469749

$vcov[[51]]
              (Intercept)             x
(Intercept)  0.0001617536 -0.0002552243
x           -0.0002552243  0.0005980651

$vcov[[52]]
              (Intercept)             x
(Intercept)  0.0002059365 -0.0002966340
x           -0.0002966340  0.0006124327

$vcov[[53]]
              (Intercept)             x
(Intercept)  0.0002257743 -0.0003243365
x           -0.0003243365  0.0006142709

$vcov[[54]]
              (Intercept)             x
(Intercept)  0.0001983986 -0.0003065649
x           -0.0003065649  0.0006387635

$vcov[[55]]
              (Intercept)             x
(Intercept)  0.0002245108 -0.0003357579
x           -0.0003357579  0.0006660109

$vcov[[56]]
              (Intercept)             x
(Intercept)  0.0002329098 -0.0003292142
x           -0.0003292142  0.0006039095

$vcov[[57]]
              (Intercept)             x
(Intercept)  0.0002459754 -0.0003454338
x           -0.0003454338  0.0006375625

$vcov[[58]]
              (Intercept)             x
(Intercept)  0.0002033512 -0.0003122884
x           -0.0003122884  0.0006302340

$vcov[[59]]
              (Intercept)             x
(Intercept)  0.0002436110 -0.0003567121
x           -0.0003567121  0.0007375679

$vcov[[60]]
              (Intercept)             x
(Intercept)  0.0002126954 -0.0003261601
x           -0.0003261601  0.0006706732

$vcov[[61]]
              (Intercept)             x
(Intercept)  0.0002201584 -0.0003344318
x           -0.0003344318  0.0006557701

$vcov[[62]]
              (Intercept)             x
(Intercept)  0.0002353309 -0.0003429726
x           -0.0003429726  0.0006707653

$vcov[[63]]
              (Intercept)             x
(Intercept)  0.0003099999 -0.0004394909
x           -0.0004394909  0.0007577738

$vcov[[64]]
              (Intercept)             x
(Intercept)  0.0002424217 -0.0003531893
x           -0.0003531893  0.0006808625

$vcov[[65]]
              (Intercept)             x
(Intercept)  0.0002649939 -0.0003753590
x           -0.0003753590  0.0006745251

$vcov[[66]]
              (Intercept)             x
(Intercept)  0.0002117032 -0.0003223112
x           -0.0003223112  0.0006174587

$vcov[[67]]
              (Intercept)             x
(Intercept)  0.0002859667 -0.0004025747
x           -0.0004025747  0.0007074014

$vcov[[68]]
              (Intercept)             x
(Intercept)  0.0001885618 -0.0003048759
x           -0.0003048759  0.0006873029

$vcov[[69]]
              (Intercept)             x
(Intercept)  0.0002286301 -0.0003573321
x           -0.0003573321  0.0007436468

$vcov[[70]]
              (Intercept)             x
(Intercept)  0.0002192830 -0.0003248851
x           -0.0003248851  0.0006704198

$vcov[[71]]
              (Intercept)             x
(Intercept)  0.0002572365 -0.0003644810
x           -0.0003644810  0.0006722963

$vcov[[72]]
              (Intercept)             x
(Intercept)  0.0002060473 -0.0003020002
x           -0.0003020002  0.0006111266

$vcov[[73]]
              (Intercept)             x
(Intercept)  0.0002454201 -0.0003747027
x           -0.0003747027  0.0007788887

$vcov[[74]]
              (Intercept)             x
(Intercept)  0.0001887984 -0.0002827344
x           -0.0002827344  0.0005903475

$vcov[[75]]
              (Intercept)             x
(Intercept)  0.0002351497 -0.0003496724
x           -0.0003496724  0.0006806999

$vcov[[76]]
              (Intercept)             x
(Intercept)  0.0002422317 -0.0003597231
x           -0.0003597231  0.0007344001

$vcov[[77]]
              (Intercept)             x
(Intercept)  0.0002405540 -0.0003502157
x           -0.0003502157  0.0006757874

$vcov[[78]]
              (Intercept)             x
(Intercept)  0.0001827395 -0.0002862686
x           -0.0002862686  0.0006332658

$vcov[[79]]
              (Intercept)             x
(Intercept)  0.0002105760 -0.0003132416
x           -0.0003132416  0.0006121368

$vcov[[80]]
              (Intercept)             x
(Intercept)  0.0002519315 -0.0003602858
x           -0.0003602858  0.0006545508

$vcov[[81]]
              (Intercept)             x
(Intercept)  0.0001990903 -0.0002869886
x           -0.0002869886  0.0005908917

$vcov[[82]]
              (Intercept)             x
(Intercept)  0.0002867552 -0.0004018213
x           -0.0004018213  0.0006944530

$vcov[[83]]
              (Intercept)             x
(Intercept)  0.0002592180 -0.0003728457
x           -0.0003728457  0.0006803025

$vcov[[84]]
              (Intercept)             x
(Intercept)  0.0002338355 -0.0003465234
x           -0.0003465234  0.0006818156

$vcov[[85]]
              (Intercept)             x
(Intercept)  0.0002573630 -0.0003908159
x           -0.0003908159  0.0007643443

$vcov[[86]]
              (Intercept)             x
(Intercept)  0.0002002175 -0.0003098824
x           -0.0003098824  0.0006583925

$vcov[[87]]
              (Intercept)             x
(Intercept)  0.0002299773 -0.0003551953
x           -0.0003551953  0.0007036858

$vcov[[88]]
              (Intercept)             x
(Intercept)  0.0002477108 -0.0003821360
x           -0.0003821360  0.0007661519

$vcov[[89]]
              (Intercept)             x
(Intercept)  0.0002257071 -0.0003448587
x           -0.0003448587  0.0007245721

$vcov[[90]]
              (Intercept)             x
(Intercept)  0.0002269427 -0.0003154283
x           -0.0003154283  0.0005756842

$vcov[[91]]
              (Intercept)             x
(Intercept)  0.0001738461 -0.0002639630
x           -0.0002639630  0.0005422297

$vcov[[92]]
              (Intercept)             x
(Intercept)  0.0002445909 -0.0003554919
x           -0.0003554919  0.0006619345

$vcov[[93]]
              (Intercept)             x
(Intercept)  0.0001817574 -0.0002944620
x           -0.0002944620  0.0006208995

$vcov[[94]]
              (Intercept)             x
(Intercept)  0.0002562979 -0.0003865247
x           -0.0003865247  0.0007755101

$vcov[[95]]
              (Intercept)             x
(Intercept)  0.0002214488 -0.0003517722
x           -0.0003517722  0.0007276381

$vcov[[96]]
              (Intercept)             x
(Intercept)  0.0002200205 -0.0003458114
x           -0.0003458114  0.0007415592

$vcov[[97]]
              (Intercept)             x
(Intercept)  0.0001703775 -0.0002556548
x           -0.0002556548  0.0005466312

$vcov[[98]]
              (Intercept)             x
(Intercept)  0.0002144528 -0.0003307649
x           -0.0003307649  0.0006854330

$vcov[[99]]
              (Intercept)             x
(Intercept)  0.0002755283 -0.0004134961
x           -0.0004134961  0.0007874229

$vcov[[100]]
              (Intercept)             x
(Intercept)  0.0002462220 -0.0003641745
x           -0.0003641745  0.0007608431

$vcov[[101]]
              (Intercept)             x
(Intercept)  0.0002894883 -0.0004282568
x           -0.0004282568  0.0008199671

$vcov[[102]]
              (Intercept)             x
(Intercept)  0.0002617580 -0.0004002256
x           -0.0004002256  0.0007910493

$vcov[[103]]
              (Intercept)             x
(Intercept)  0.0002018273 -0.0003026911
x           -0.0003026911  0.0005931943

$vcov[[104]]
              (Intercept)             x
(Intercept)  0.0002673874 -0.0004035133
x           -0.0004035133  0.0007630534

$vcov[[105]]
              (Intercept)             x
(Intercept)  0.0002522805 -0.0003893157
x           -0.0003893157  0.0007319531

$vcov[[106]]
              (Intercept)             x
(Intercept)  0.0002410740 -0.0003549662
x           -0.0003549662  0.0007164527

$vcov[[107]]
              (Intercept)             x
(Intercept)  0.0002130826 -0.0003109011
x           -0.0003109011  0.0005779572

$vcov[[108]]
              (Intercept)             x
(Intercept)  0.0002422422 -0.0003562611
x           -0.0003562611  0.0006696448

$vcov[[109]]
              (Intercept)             x
(Intercept)  0.0002202304 -0.0003212298
x           -0.0003212298  0.0006495960

$vcov[[110]]
              (Intercept)             x
(Intercept)  0.0001788101 -0.0002806163
x           -0.0002806163  0.0005845040

$vcov[[111]]
              (Intercept)             x
(Intercept)  0.0002343651 -0.0003420091
x           -0.0003420091  0.0006576039

$vcov[[112]]
              (Intercept)             x
(Intercept)  0.0001847849 -0.0002676011
x           -0.0002676011  0.0005262390

$vcov[[113]]
              (Intercept)             x
(Intercept)  0.0002446286 -0.0003563524
x           -0.0003563524  0.0006764532

$vcov[[114]]
              (Intercept)             x
(Intercept)  0.0002730768 -0.0003990804
x           -0.0003990804  0.0008235303

$vcov[[115]]
              (Intercept)             x
(Intercept)  0.0001971983 -0.0003094724
x           -0.0003094724  0.0006610469

$vcov[[116]]
              (Intercept)             x
(Intercept)  0.0002653922 -0.0003985997
x           -0.0003985997  0.0007691242

$vcov[[117]]
              (Intercept)             x
(Intercept)  0.0002345479 -0.0003650334
x           -0.0003650334  0.0007686095

$vcov[[118]]
              (Intercept)             x
(Intercept)  0.0002056989 -0.0002990698
x           -0.0002990698  0.0005975572

$vcov[[119]]
              (Intercept)            x
(Intercept)  0.0001699568 -0.000275687
x           -0.0002756870  0.000607975

$vcov[[120]]
              (Intercept)             x
(Intercept)  0.0001905824 -0.0002876883
x           -0.0002876883  0.0005990373

$vcov[[121]]
              (Intercept)             x
(Intercept)  0.0002247386 -0.0003313644
x           -0.0003313644  0.0006376478

$vcov[[122]]
              (Intercept)             x
(Intercept)  0.0002431357 -0.0003519575
x           -0.0003519575  0.0006712105

$vcov[[123]]
              (Intercept)             x
(Intercept)  0.0002191420 -0.0003382722
x           -0.0003382722  0.0006562387

$vcov[[124]]
              (Intercept)             x
(Intercept)  0.0002507173 -0.0003835640
x           -0.0003835640  0.0007662279

$vcov[[125]]
              (Intercept)             x
(Intercept)  0.0002805586 -0.0003996150
x           -0.0003996150  0.0007091647

$vcov[[126]]
              (Intercept)             x
(Intercept)  0.0002048761 -0.0003220356
x           -0.0003220356  0.0006759125

$vcov[[127]]
              (Intercept)             x
(Intercept)  0.0002423591 -0.0003615057
x           -0.0003615057  0.0007128238

$vcov[[128]]
              (Intercept)             x
(Intercept)  0.0002094898 -0.0003083388
x           -0.0003083388  0.0005910285

$vcov[[129]]
              (Intercept)             x
(Intercept)  0.0001898640 -0.0002910785
x           -0.0002910785  0.0006199379

$vcov[[130]]
              (Intercept)             x
(Intercept)  0.0001868736 -0.0002982931
x           -0.0002982931  0.0006610336

$vcov[[131]]
              (Intercept)             x
(Intercept)  0.0001889830 -0.0002916945
x           -0.0002916945  0.0006507766

$vcov[[132]]
              (Intercept)             x
(Intercept)  0.0002540694 -0.0003659039
x           -0.0003659039  0.0007056808

$vcov[[133]]
              (Intercept)             x
(Intercept)  0.0002504997 -0.0003744482
x           -0.0003744482  0.0007444022

$vcov[[134]]
              (Intercept)             x
(Intercept)  0.0002291392 -0.0003429455
x           -0.0003429455  0.0006703156

$vcov[[135]]
              (Intercept)             x
(Intercept)  0.0002453927 -0.0003628757
x           -0.0003628757  0.0006932502

$vcov[[136]]
              (Intercept)             x
(Intercept)  0.0002763340 -0.0003706421
x           -0.0003706421  0.0006285153

$vcov[[137]]
              (Intercept)             x
(Intercept)  0.0002945632 -0.0004138236
x           -0.0004138236  0.0007259292

$vcov[[138]]
              (Intercept)             x
(Intercept)  0.0002956886 -0.0004121747
x           -0.0004121747  0.0007555904

$vcov[[139]]
              (Intercept)             x
(Intercept)  0.0002153086 -0.0003302475
x           -0.0003302475  0.0006630350

$vcov[[140]]
              (Intercept)             x
(Intercept)  0.0002024908 -0.0003207979
x           -0.0003207979  0.0006589786

$vcov[[141]]
              (Intercept)             x
(Intercept)  0.0002090617 -0.0003292443
x           -0.0003292443  0.0007126293

$vcov[[142]]
              (Intercept)             x
(Intercept)  0.0001815570 -0.0002808153
x           -0.0002808153  0.0005731224

$vcov[[143]]
              (Intercept)             x
(Intercept)  0.0002450905 -0.0003716943
x           -0.0003716943  0.0007503414

$vcov[[144]]
              (Intercept)             x
(Intercept)  0.0002745943 -0.0004092528
x           -0.0004092528  0.0007966335

$vcov[[145]]
              (Intercept)             x
(Intercept)  0.0002346822 -0.0003459856
x           -0.0003459856  0.0006900651

$vcov[[146]]
              (Intercept)             x
(Intercept)  0.0001960116 -0.0003269356
x           -0.0003269356  0.0007505601

$vcov[[147]]
              (Intercept)             x
(Intercept)  0.0001929585 -0.0002921590
x           -0.0002921590  0.0005637807

$vcov[[148]]
              (Intercept)             x
(Intercept)  0.0002421877 -0.0003385491
x           -0.0003385491  0.0005901520

$vcov[[149]]
              (Intercept)             x
(Intercept)  0.0001969502 -0.0003107291
x           -0.0003107291  0.0006990614

$vcov[[150]]
              (Intercept)             x
(Intercept)  0.0002310414 -0.0003442472
x           -0.0003442472  0.0006875845

$vcov[[151]]
              (Intercept)             x
(Intercept)  0.0002863494 -0.0004008845
x           -0.0004008845  0.0007208114

$vcov[[152]]
              (Intercept)             x
(Intercept)  0.0002323150 -0.0003412499
x           -0.0003412499  0.0006422814

$vcov[[153]]
              (Intercept)             x
(Intercept)  0.0002283363 -0.0003358974
x           -0.0003358974  0.0006640690

$vcov[[154]]
              (Intercept)             x
(Intercept)  0.0002505739 -0.0003622594
x           -0.0003622594  0.0006896577

$vcov[[155]]
              (Intercept)             x
(Intercept)  0.0002123548 -0.0003230835
x           -0.0003230835  0.0006680183

$vcov[[156]]
              (Intercept)             x
(Intercept)  0.0002036828 -0.0003126501
x           -0.0003126501  0.0006321132

$vcov[[157]]
              (Intercept)             x
(Intercept)  0.0002262104 -0.0003474091
x           -0.0003474091  0.0006739376

$vcov[[158]]
              (Intercept)             x
(Intercept)  0.0002809863 -0.0004042105
x           -0.0004042105  0.0007042362

$vcov[[159]]
              (Intercept)             x
(Intercept)  0.0002481685 -0.0003857034
x           -0.0003857034  0.0007733386

$vcov[[160]]
              (Intercept)             x
(Intercept)  0.0002129794 -0.0003199933
x           -0.0003199933  0.0006503673

$vcov[[161]]
              (Intercept)             x
(Intercept)  0.0002179792 -0.0003129530
x           -0.0003129530  0.0006244165

$vcov[[162]]
              (Intercept)             x
(Intercept)  0.0003114342 -0.0004502618
x           -0.0004502618  0.0008068186

$vcov[[163]]
              (Intercept)             x
(Intercept)  0.0001962529 -0.0003066384
x           -0.0003066384  0.0006494521

$vcov[[164]]
              (Intercept)             x
(Intercept)  0.0002606597 -0.0003915137
x           -0.0003915137  0.0007462907

$vcov[[165]]
              (Intercept)             x
(Intercept)  0.0002176373 -0.0003257732
x           -0.0003257732  0.0006619899

$vcov[[166]]
              (Intercept)             x
(Intercept)  0.0001985387 -0.0003102746
x           -0.0003102746  0.0006714376

$vcov[[167]]
              (Intercept)             x
(Intercept)  0.0001862880 -0.0002777471
x           -0.0002777471  0.0005427319

$vcov[[168]]
              (Intercept)             x
(Intercept)  0.0002395010 -0.0003397806
x           -0.0003397806  0.0006494233

$vcov[[169]]
              (Intercept)             x
(Intercept)  0.0002213363 -0.0003388724
x           -0.0003388724  0.0006629209

$vcov[[170]]
              (Intercept)             x
(Intercept)  0.0002284513 -0.0003505793
x           -0.0003505793  0.0007076044

$vcov[[171]]
              (Intercept)             x
(Intercept)  0.0002443218 -0.0003797090
x           -0.0003797090  0.0007777521

$vcov[[172]]
              (Intercept)             x
(Intercept)  0.0002343744 -0.0003613374
x           -0.0003613374  0.0007306222

$vcov[[173]]
              (Intercept)             x
(Intercept)  0.0003033504 -0.0004268975
x           -0.0004268975  0.0007638461

$vcov[[174]]
              (Intercept)             x
(Intercept)  0.0002296356 -0.0003432833
x           -0.0003432833  0.0006772892

$vcov[[175]]
              (Intercept)             x
(Intercept)  0.0002314485 -0.0003586664
x           -0.0003586664  0.0007578870

$vcov[[176]]
              (Intercept)             x
(Intercept)  0.0002317901 -0.0003510925
x           -0.0003510925  0.0007019256

$vcov[[177]]
              (Intercept)             x
(Intercept)  0.0001935738 -0.0003039250
x           -0.0003039250  0.0006205337

$vcov[[178]]
              (Intercept)             x
(Intercept)  0.0002798533 -0.0004074646
x           -0.0004074646  0.0007631978

$vcov[[179]]
              (Intercept)             x
(Intercept)  0.0002193156 -0.0003406798
x           -0.0003406798  0.0006979933

$vcov[[180]]
              (Intercept)             x
(Intercept)  0.0002054939 -0.0003033064
x           -0.0003033064  0.0006215429

$vcov[[181]]
              (Intercept)             x
(Intercept)  0.0002256173 -0.0003438297
x           -0.0003438297  0.0007074341

$vcov[[182]]
              (Intercept)             x
(Intercept)  0.0002343572 -0.0003556627
x           -0.0003556627  0.0007181690

$vcov[[183]]
              (Intercept)             x
(Intercept)  0.0002173729 -0.0003289017
x           -0.0003289017  0.0006469975

$vcov[[184]]
              (Intercept)             x
(Intercept)  0.0002246686 -0.0003376895
x           -0.0003376895  0.0007046804

$vcov[[185]]
             (Intercept)             x
(Intercept)  0.000240201 -0.0003457330
x           -0.000345733  0.0006500156

$vcov[[186]]
              (Intercept)             x
(Intercept)  0.0002268652 -0.0003209615
x           -0.0003209615  0.0006031243

$vcov[[187]]
              (Intercept)             x
(Intercept)  0.0002011717 -0.0003147273
x           -0.0003147273  0.0006507673

$vcov[[188]]
              (Intercept)             x
(Intercept)  0.0002275953 -0.0003589099
x           -0.0003589099  0.0007369483

$vcov[[189]]
              (Intercept)             x
(Intercept)  0.0002969248 -0.0004534419
x           -0.0004534419  0.0008973571

$vcov[[190]]
             (Intercept)             x
(Intercept)  0.000250151 -0.0003642640
x           -0.000364264  0.0006965896

$vcov[[191]]
              (Intercept)             x
(Intercept)  0.0002040152 -0.0003168604
x           -0.0003168604  0.0006880738

$vcov[[192]]
              (Intercept)             x
(Intercept)  0.0002052854 -0.0003196432
x           -0.0003196432  0.0006564333

$vcov[[193]]
              (Intercept)             x
(Intercept)  0.0002848255 -0.0004145541
x           -0.0004145541  0.0008069963

$vcov[[194]]
              (Intercept)             x
(Intercept)  0.0001995615 -0.0002964541
x           -0.0002964541  0.0005819469

$vcov[[195]]
              (Intercept)             x
(Intercept)  0.0002375654 -0.0003576816
x           -0.0003576816  0.0007368687

$vcov[[196]]
              (Intercept)             x
(Intercept)  0.0002177842 -0.0003284412
x           -0.0003284412  0.0006676953

$vcov[[197]]
              (Intercept)             x
(Intercept)  0.0001767124 -0.0002707254
x           -0.0002707254  0.0006221786

$vcov[[198]]
              (Intercept)             x
(Intercept)  0.0002556934 -0.0003796756
x           -0.0003796756  0.0007618736

$vcov[[199]]
              (Intercept)             x
(Intercept)  0.0002785588 -0.0004085862
x           -0.0004085862  0.0007678987

$vcov[[200]]
              (Intercept)             x
(Intercept)  0.0002493072 -0.0003616520
x           -0.0003616520  0.0006988958

$vcov[[201]]
              (Intercept)             x
(Intercept)  0.0002101533 -0.0003203058
x           -0.0003203058  0.0006473640

$vcov[[202]]
              (Intercept)             x
(Intercept)  0.0002559088 -0.0003570100
x           -0.0003570100  0.0006914788

$vcov[[203]]
              (Intercept)             x
(Intercept)  0.0003078538 -0.0004496294
x           -0.0004496294  0.0007874181

$vcov[[204]]
              (Intercept)             x
(Intercept)  0.0002470853 -0.0003651907
x           -0.0003651907  0.0007053986

$vcov[[205]]
              (Intercept)             x
(Intercept)  0.0002880380 -0.0004266145
x           -0.0004266145  0.0008158509

$vcov[[206]]
              (Intercept)             x
(Intercept)  0.0002387949 -0.0003575660
x           -0.0003575660  0.0007097941

$vcov[[207]]
              (Intercept)             x
(Intercept)  0.0001496387 -0.0002423873
x           -0.0002423873  0.0005764849

$vcov[[208]]
              (Intercept)             x
(Intercept)  0.0002350107 -0.0003770201
x           -0.0003770201  0.0007677692

$vcov[[209]]
              (Intercept)             x
(Intercept)  0.0002498519 -0.0003586102
x           -0.0003586102  0.0006997840

$vcov[[210]]
              (Intercept)             x
(Intercept)  0.0002496791 -0.0003620727
x           -0.0003620727  0.0006797609

$vcov[[211]]
              (Intercept)             x
(Intercept)  0.0002326114 -0.0003532754
x           -0.0003532754  0.0007030528

$vcov[[212]]
              (Intercept)             x
(Intercept)  0.0002235092 -0.0003309012
x           -0.0003309012  0.0006474479

$vcov[[213]]
              (Intercept)             x
(Intercept)  0.0002219025 -0.0003271557
x           -0.0003271557  0.0006618411

$vcov[[214]]
              (Intercept)             x
(Intercept)  0.0002189668 -0.0003366616
x           -0.0003366616  0.0007132779

$vcov[[215]]
              (Intercept)             x
(Intercept)  0.0002088711 -0.0003144850
x           -0.0003144850  0.0006514494

$vcov[[216]]
              (Intercept)             x
(Intercept)  0.0002024043 -0.0003221356
x           -0.0003221356  0.0006859466

$vcov[[217]]
              (Intercept)             x
(Intercept)  0.0002425272 -0.0003732856
x           -0.0003732856  0.0007676422

$vcov[[218]]
              (Intercept)             x
(Intercept)  0.0002585937 -0.0003775644
x           -0.0003775644  0.0007286952

$vcov[[219]]
              (Intercept)             x
(Intercept)  0.0001707454 -0.0002741397
x           -0.0002741397  0.0006554384

$vcov[[220]]
              (Intercept)             x
(Intercept)  0.0002061871 -0.0003104381
x           -0.0003104381  0.0006468342

$vcov[[221]]
              (Intercept)             x
(Intercept)  0.0002417004 -0.0003576020
x           -0.0003576020  0.0007178216

$vcov[[222]]
              (Intercept)             x
(Intercept)  0.0002377521 -0.0003542929
x           -0.0003542929  0.0007212480

$vcov[[223]]
              (Intercept)             x
(Intercept)  0.0002304843 -0.0003487890
x           -0.0003487890  0.0007553722

$vcov[[224]]
              (Intercept)             x
(Intercept)  0.0002147140 -0.0003278136
x           -0.0003278136  0.0006724800

$vcov[[225]]
              (Intercept)             x
(Intercept)  0.0001951228 -0.0002959798
x           -0.0002959798  0.0005886131

$vcov[[226]]
              (Intercept)             x
(Intercept)  0.0002564865 -0.0003892899
x           -0.0003892899  0.0007835757

$vcov[[227]]
              (Intercept)             x
(Intercept)  0.0002031829 -0.0003147937
x           -0.0003147937  0.0006514915

$vcov[[228]]
              (Intercept)             x
(Intercept)  0.0001942763 -0.0003045753
x           -0.0003045753  0.0006201254

$vcov[[229]]
              (Intercept)             x
(Intercept)  0.0002386060 -0.0003535871
x           -0.0003535871  0.0007043955

$vcov[[230]]
              (Intercept)             x
(Intercept)  0.0002117684 -0.0003250211
x           -0.0003250211  0.0006538304

$vcov[[231]]
              (Intercept)             x
(Intercept)  0.0002413446 -0.0003464759
x           -0.0003464759  0.0006659992

$vcov[[232]]
              (Intercept)             x
(Intercept)  0.0002364815 -0.0003350775
x           -0.0003350775  0.0006464562

$vcov[[233]]
              (Intercept)             x
(Intercept)  0.0002503567 -0.0003954242
x           -0.0003954242  0.0008193164

$vcov[[234]]
              (Intercept)             x
(Intercept)  0.0002784761 -0.0004124591
x           -0.0004124591  0.0007902460

$vcov[[235]]
              (Intercept)             x
(Intercept)  0.0002741550 -0.0004016917
x           -0.0004016917  0.0007462965

$vcov[[236]]
              (Intercept)             x
(Intercept)  0.0002501602 -0.0003739805
x           -0.0003739805  0.0007488065

$vcov[[237]]
              (Intercept)             x
(Intercept)  0.0001839492 -0.0002882371
x           -0.0002882371  0.0006207087

$vcov[[238]]
             (Intercept)             x
(Intercept)  0.000241448 -0.0003785720
x           -0.000378572  0.0007712075

$vcov[[239]]
              (Intercept)             x
(Intercept)  0.0002323466 -0.0003525488
x           -0.0003525488  0.0007127429

$vcov[[240]]
              (Intercept)             x
(Intercept)  0.0002397966 -0.0003679645
x           -0.0003679645  0.0007170052

$vcov[[241]]
              (Intercept)             x
(Intercept)  0.0002496643 -0.0003783303
x           -0.0003783303  0.0007287942

$vcov[[242]]
              (Intercept)             x
(Intercept)  0.0002050017 -0.0003186978
x           -0.0003186978  0.0006865362

$vcov[[243]]
              (Intercept)             x
(Intercept)  0.0002313614 -0.0003417823
x           -0.0003417823  0.0006563036

$vcov[[244]]
              (Intercept)             x
(Intercept)  0.0002013617 -0.0003252243
x           -0.0003252243  0.0006818735

$vcov[[245]]
              (Intercept)             x
(Intercept)  0.0002436308 -0.0003739943
x           -0.0003739943  0.0007580115

$vcov[[246]]
              (Intercept)             x
(Intercept)  0.0002058327 -0.0003305124
x           -0.0003305124  0.0007509346

$vcov[[247]]
              (Intercept)             x
(Intercept)  0.0003271673 -0.0004772412
x           -0.0004772412  0.0009073637

$vcov[[248]]
              (Intercept)             x
(Intercept)  0.0002496727 -0.0003795729
x           -0.0003795729  0.0007651582

$vcov[[249]]
              (Intercept)             x
(Intercept)  0.0002462041 -0.0003608707
x           -0.0003608707  0.0007101487

$vcov[[250]]
              (Intercept)             x
(Intercept)  0.0001805003 -0.0002961695
x           -0.0002961695  0.0007060223

$vcov[[251]]
              (Intercept)             x
(Intercept)  0.0001884103 -0.0002967835
x           -0.0002967835  0.0006470497

$vcov[[252]]
              (Intercept)             x
(Intercept)  0.0002109327 -0.0003230055
x           -0.0003230055  0.0006883136

$vcov[[253]]
              (Intercept)             x
(Intercept)  0.0002021491 -0.0003050661
x           -0.0003050661  0.0006390468

$vcov[[254]]
              (Intercept)             x
(Intercept)  0.0002256714 -0.0003242296
x           -0.0003242296  0.0006427489

$vcov[[255]]
              (Intercept)             x
(Intercept)  0.0002134010 -0.0003212107
x           -0.0003212107  0.0006027918

$vcov[[256]]
              (Intercept)             x
(Intercept)  0.0002313358 -0.0003569260
x           -0.0003569260  0.0007505824

$vcov[[257]]
              (Intercept)             x
(Intercept)  0.0002514900 -0.0003520366
x           -0.0003520366  0.0006363730

$vcov[[258]]
              (Intercept)             x
(Intercept)  0.0001909883 -0.0002864300
x           -0.0002864300  0.0005982679

$vcov[[259]]
              (Intercept)             x
(Intercept)  0.0001846357 -0.0002799589
x           -0.0002799589  0.0005671345

$vcov[[260]]
              (Intercept)             x
(Intercept)  0.0002657794 -0.0003847869
x           -0.0003847869  0.0007026614

$vcov[[261]]
              (Intercept)             x
(Intercept)  0.0002307381 -0.0003316381
x           -0.0003316381  0.0006442190

$vcov[[262]]
              (Intercept)             x
(Intercept)  0.0002432847 -0.0003620192
x           -0.0003620192  0.0007164647

$vcov[[263]]
              (Intercept)             x
(Intercept)  0.0002414510 -0.0003505468
x           -0.0003505468  0.0006572518

$vcov[[264]]
              (Intercept)             x
(Intercept)  0.0002219046 -0.0003465837
x           -0.0003465837  0.0007273431

$vcov[[265]]
              (Intercept)             x
(Intercept)  0.0002086649 -0.0003153421
x           -0.0003153421  0.0006550479

$vcov[[266]]
              (Intercept)             x
(Intercept)  0.0002058968 -0.0002957418
x           -0.0002957418  0.0005637795

$vcov[[267]]
              (Intercept)             x
(Intercept)  0.0002414299 -0.0003614316
x           -0.0003614316  0.0006856584

$vcov[[268]]
              (Intercept)             x
(Intercept)  0.0001889117 -0.0002984628
x           -0.0002984628  0.0006432733

$vcov[[269]]
              (Intercept)             x
(Intercept)  0.0002132886 -0.0003035617
x           -0.0003035617  0.0005673928

$vcov[[270]]
              (Intercept)             x
(Intercept)  0.0002807754 -0.0004050263
x           -0.0004050263  0.0007576257

$vcov[[271]]
              (Intercept)             x
(Intercept)  0.0002536981 -0.0003987085
x           -0.0003987085  0.0008359728

$vcov[[272]]
              (Intercept)             x
(Intercept)  0.0002329541 -0.0003642679
x           -0.0003642679  0.0007222600

$vcov[[273]]
              (Intercept)             x
(Intercept)  0.0001693351 -0.0002714829
x           -0.0002714829  0.0006180208

$vcov[[274]]
              (Intercept)             x
(Intercept)  0.0001901461 -0.0002854116
x           -0.0002854116  0.0005967708

$vcov[[275]]
              (Intercept)             x
(Intercept)  0.0002610274 -0.0003937901
x           -0.0003937901  0.0007493824

$vcov[[276]]
              (Intercept)             x
(Intercept)  0.0002465245 -0.0003788548
x           -0.0003788548  0.0007536851

$vcov[[277]]
              (Intercept)             x
(Intercept)  0.0002599954 -0.0003992854
x           -0.0003992854  0.0008230517

$vcov[[278]]
              (Intercept)             x
(Intercept)  0.0001896431 -0.0003012713
x           -0.0003012713  0.0006452388

$vcov[[279]]
              (Intercept)             x
(Intercept)  0.0002415629 -0.0003618028
x           -0.0003618028  0.0006824951

$vcov[[280]]
              (Intercept)             x
(Intercept)  0.0002109317 -0.0003413683
x           -0.0003413683  0.0007779337

$vcov[[281]]
              (Intercept)             x
(Intercept)  0.0002503940 -0.0003772677
x           -0.0003772677  0.0007772536

$vcov[[282]]
              (Intercept)             x
(Intercept)  0.0002058743 -0.0003164673
x           -0.0003164673  0.0006290640

$vcov[[283]]
              (Intercept)             x
(Intercept)  0.0002579032 -0.0003853942
x           -0.0003853942  0.0007478757

$vcov[[284]]
              (Intercept)             x
(Intercept)  0.0002278892 -0.0003596030
x           -0.0003596030  0.0007408875

$vcov[[285]]
              (Intercept)             x
(Intercept)  0.0002094162 -0.0003288222
x           -0.0003288222  0.0006654376

$vcov[[286]]
              (Intercept)             x
(Intercept)  0.0001991654 -0.0003198774
x           -0.0003198774  0.0007306236

$vcov[[287]]
              (Intercept)             x
(Intercept)  0.0002280230 -0.0003366894
x           -0.0003366894  0.0007143599

$vcov[[288]]
              (Intercept)             x
(Intercept)  0.0002327866 -0.0003475373
x           -0.0003475373  0.0006939785

$vcov[[289]]
              (Intercept)             x
(Intercept)  0.0001958363 -0.0002946776
x           -0.0002946776  0.0006334261

$vcov[[290]]
              (Intercept)             x
(Intercept)  0.0002390113 -0.0003498538
x           -0.0003498538  0.0006745773

$vcov[[291]]
              (Intercept)             x
(Intercept)  0.0002269013 -0.0003308018
x           -0.0003308018  0.0006390124

$vcov[[292]]
              (Intercept)             x
(Intercept)  0.0002407708 -0.0003378821
x           -0.0003378821  0.0006331620

$vcov[[293]]
              (Intercept)             x
(Intercept)  0.0002113720 -0.0003382732
x           -0.0003382732  0.0007075159

$vcov[[294]]
              (Intercept)             x
(Intercept)  0.0002138752 -0.0003399236
x           -0.0003399236  0.0006968275

$vcov[[295]]
              (Intercept)             x
(Intercept)  0.0002285749 -0.0003391983
x           -0.0003391983  0.0006923329

$vcov[[296]]
              (Intercept)             x
(Intercept)  0.0001986829 -0.0003130299
x           -0.0003130299  0.0006902153

$vcov[[297]]
              (Intercept)             x
(Intercept)  0.0002342099 -0.0003479686
x           -0.0003479686  0.0006843826

$vcov[[298]]
              (Intercept)             x
(Intercept)  0.0002263872 -0.0003298466
x           -0.0003298466  0.0006179841

$vcov[[299]]
              (Intercept)             x
(Intercept)  0.0002432687 -0.0003792890
x           -0.0003792890  0.0007884058

$vcov[[300]]
              (Intercept)             x
(Intercept)  0.0002245073 -0.0003474876
x           -0.0003474876  0.0007570653

$vcov[[301]]
              (Intercept)            x
(Intercept)  0.0002106422 -0.000319863
x           -0.0003198630  0.000655396

$vcov[[302]]
              (Intercept)             x
(Intercept)  0.0002250694 -0.0003404127
x           -0.0003404127  0.0006565572

$vcov[[303]]
              (Intercept)             x
(Intercept)  0.0002171306 -0.0003435901
x           -0.0003435901  0.0007656199

$vcov[[304]]
              (Intercept)             x
(Intercept)  0.0002122977 -0.0003080464
x           -0.0003080464  0.0005899283

$vcov[[305]]
              (Intercept)             x
(Intercept)  0.0001783445 -0.0002752202
x           -0.0002752202  0.0006063333

$vcov[[306]]
              (Intercept)             x
(Intercept)  0.0002156409 -0.0003197075
x           -0.0003197075  0.0006151706

$vcov[[307]]
              (Intercept)             x
(Intercept)  0.0002237123 -0.0003421217
x           -0.0003421217  0.0007267430

$vcov[[308]]
              (Intercept)             x
(Intercept)  0.0002113860 -0.0003342536
x           -0.0003342536  0.0007151375

$vcov[[309]]
              (Intercept)             x
(Intercept)  0.0001908803 -0.0002950469
x           -0.0002950469  0.0006291906

$vcov[[310]]
              (Intercept)             x
(Intercept)  0.0002153532 -0.0003261993
x           -0.0003261993  0.0006833420

$vcov[[311]]
              (Intercept)             x
(Intercept)  0.0003036383 -0.0004311371
x           -0.0004311371  0.0007583762

$vcov[[312]]
              (Intercept)             x
(Intercept)  0.0002645843 -0.0003839020
x           -0.0003839020  0.0006996236

$vcov[[313]]
              (Intercept)             x
(Intercept)  0.0002463655 -0.0003624354
x           -0.0003624354  0.0007548744

$vcov[[314]]
              (Intercept)             x
(Intercept)  0.0002811918 -0.0004151233
x           -0.0004151233  0.0007801874

$vcov[[315]]
              (Intercept)             x
(Intercept)  0.0001986534 -0.0002830829
x           -0.0002830829  0.0005616856

$vcov[[316]]
              (Intercept)             x
(Intercept)  0.0002672359 -0.0003993014
x           -0.0003993014  0.0007883700

$vcov[[317]]
              (Intercept)             x
(Intercept)  0.0002303903 -0.0003492055
x           -0.0003492055  0.0006967899

$vcov[[318]]
              (Intercept)             x
(Intercept)  0.0002341059 -0.0003437787
x           -0.0003437787  0.0006227624

$vcov[[319]]
              (Intercept)             x
(Intercept)  0.0002377098 -0.0003617857
x           -0.0003617857  0.0007613545

$vcov[[320]]
              (Intercept)             x
(Intercept)  0.0002165182 -0.0003348112
x           -0.0003348112  0.0006717221

$vcov[[321]]
              (Intercept)             x
(Intercept)  0.0002042377 -0.0002949315
x           -0.0002949315  0.0005536244

$vcov[[322]]
              (Intercept)             x
(Intercept)  0.0002625846 -0.0004152410
x           -0.0004152410  0.0008710396

$vcov[[323]]
              (Intercept)             x
(Intercept)  0.0002003850 -0.0003001073
x           -0.0003001073  0.0006054124

$vcov[[324]]
              (Intercept)             x
(Intercept)  0.0002037019 -0.0003025809
x           -0.0003025809  0.0006330505

$vcov[[325]]
              (Intercept)             x
(Intercept)  0.0002778805 -0.0003957398
x           -0.0003957398  0.0007334672

$vcov[[326]]
              (Intercept)             x
(Intercept)  0.0002287172 -0.0003313399
x           -0.0003313399  0.0006100639

$vcov[[327]]
              (Intercept)             x
(Intercept)  0.0002493770 -0.0003605829
x           -0.0003605829  0.0006922735

$vcov[[328]]
              (Intercept)             x
(Intercept)  0.0002099083 -0.0003209875
x           -0.0003209875  0.0006543080

$vcov[[329]]
              (Intercept)             x
(Intercept)  0.0002928401 -0.0004165228
x           -0.0004165228  0.0007607593

$vcov[[330]]
              (Intercept)             x
(Intercept)  0.0002672769 -0.0004265563
x           -0.0004265563  0.0008750062

$vcov[[331]]
              (Intercept)             x
(Intercept)  0.0002075382 -0.0003299704
x           -0.0003299704  0.0006991670

$vcov[[332]]
              (Intercept)             x
(Intercept)  0.0002509727 -0.0003757391
x           -0.0003757391  0.0007494882

$vcov[[333]]
              (Intercept)             x
(Intercept)  0.0002131916 -0.0003050025
x           -0.0003050025  0.0005950165

$vcov[[334]]
              (Intercept)             x
(Intercept)  0.0001938518 -0.0002908987
x           -0.0002908987  0.0006209634

$vcov[[335]]
              (Intercept)             x
(Intercept)  0.0001941580 -0.0002873867
x           -0.0002873867  0.0005856845

$vcov[[336]]
              (Intercept)             x
(Intercept)  0.0002178833 -0.0003382153
x           -0.0003382153  0.0007103874

$vcov[[337]]
              (Intercept)             x
(Intercept)  0.0001941106 -0.0002848092
x           -0.0002848092  0.0005666853

$vcov[[338]]
              (Intercept)             x
(Intercept)  0.0002802541 -0.0004022322
x           -0.0004022322  0.0007376518

$vcov[[339]]
              (Intercept)             x
(Intercept)  0.0002007134 -0.0003013428
x           -0.0003013428  0.0006013325

$vcov[[340]]
              (Intercept)             x
(Intercept)  0.0002363617 -0.0003506413
x           -0.0003506413  0.0007165154

$vcov[[341]]
              (Intercept)             x
(Intercept)  0.0001979170 -0.0002961681
x           -0.0002961681  0.0005864107

$vcov[[342]]
              (Intercept)             x
(Intercept)  0.0001931923 -0.0002935987
x           -0.0002935987  0.0006407579

$vcov[[343]]
              (Intercept)             x
(Intercept)  0.0002156726 -0.0003374403
x           -0.0003374403  0.0007175070

$vcov[[344]]
              (Intercept)             x
(Intercept)  0.0002154237 -0.0003309689
x           -0.0003309689  0.0007118443

$vcov[[345]]
              (Intercept)             x
(Intercept)  0.0002640832 -0.0003807280
x           -0.0003807280  0.0006857312

$vcov[[346]]
              (Intercept)             x
(Intercept)  0.0001730849 -0.0002800961
x           -0.0002800961  0.0005993736

$vcov[[347]]
              (Intercept)             x
(Intercept)  0.0002389282 -0.0003560901
x           -0.0003560901  0.0007018856

$vcov[[348]]
             (Intercept)             x
(Intercept)  0.000217281 -0.0003267120
x           -0.000326712  0.0006778119

$vcov[[349]]
              (Intercept)             x
(Intercept)  0.0002403486 -0.0003705122
x           -0.0003705122  0.0007209124

$vcov[[350]]
              (Intercept)             x
(Intercept)  0.0002165511 -0.0003228757
x           -0.0003228757  0.0006553063

$vcov[[351]]
              (Intercept)             x
(Intercept)  0.0001758501 -0.0002750046
x           -0.0002750046  0.0006267780

$vcov[[352]]
              (Intercept)             x
(Intercept)  0.0001966465 -0.0002936232
x           -0.0002936232  0.0006088388

$vcov[[353]]
              (Intercept)             x
(Intercept)  0.0002580482 -0.0003762030
x           -0.0003762030  0.0007230701

$vcov[[354]]
              (Intercept)             x
(Intercept)  0.0002183939 -0.0003247516
x           -0.0003247516  0.0006345474

$vcov[[355]]
              (Intercept)             x
(Intercept)  0.0002476784 -0.0003692399
x           -0.0003692399  0.0007204583

$vcov[[356]]
              (Intercept)             x
(Intercept)  0.0002293497 -0.0003441307
x           -0.0003441307  0.0007055778

$vcov[[357]]
              (Intercept)             x
(Intercept)  0.0003132964 -0.0004314064
x           -0.0004314064  0.0007510548

$vcov[[358]]
              (Intercept)             x
(Intercept)  0.0002493328 -0.0003609936
x           -0.0003609936  0.0006874978

$vcov[[359]]
              (Intercept)             x
(Intercept)  0.0001957580 -0.0002877645
x           -0.0002877645  0.0005771268

$vcov[[360]]
              (Intercept)             x
(Intercept)  0.0002195512 -0.0003416293
x           -0.0003416293  0.0006725538

$vcov[[361]]
              (Intercept)             x
(Intercept)  0.0002325055 -0.0003333937
x           -0.0003333937  0.0006590208

$vcov[[362]]
              (Intercept)             x
(Intercept)  0.0002296748 -0.0003339213
x           -0.0003339213  0.0006123713

$vcov[[363]]
              (Intercept)             x
(Intercept)  0.0002048447 -0.0002986340
x           -0.0002986340  0.0005679049

$vcov[[364]]
              (Intercept)             x
(Intercept)  0.0002529980 -0.0003797049
x           -0.0003797049  0.0007279526

$vcov[[365]]
              (Intercept)             x
(Intercept)  0.0002071695 -0.0003093493
x           -0.0003093493  0.0006362133

$vcov[[366]]
              (Intercept)             x
(Intercept)  0.0001827772 -0.0002837453
x           -0.0002837453  0.0006255318

$vcov[[367]]
              (Intercept)             x
(Intercept)  0.0002131851 -0.0003282028
x           -0.0003282028  0.0006937481

$vcov[[368]]
              (Intercept)             x
(Intercept)  0.0002160966 -0.0003358560
x           -0.0003358560  0.0006700156

$vcov[[369]]
              (Intercept)             x
(Intercept)  0.0002262739 -0.0003262904
x           -0.0003262904  0.0006502614

$vcov[[370]]
              (Intercept)             x
(Intercept)  0.0002555480 -0.0003933185
x           -0.0003933185  0.0008168641

$vcov[[371]]
              (Intercept)             x
(Intercept)  0.0002254058 -0.0003624186
x           -0.0003624186  0.0007532911

$vcov[[372]]
             (Intercept)             x
(Intercept)  0.000254767 -0.0003800020
x           -0.000380002  0.0007600405

$vcov[[373]]
              (Intercept)             x
(Intercept)  0.0002117951 -0.0003122257
x           -0.0003122257  0.0006219090

$vcov[[374]]
              (Intercept)             x
(Intercept)  0.0001965999 -0.0003041105
x           -0.0003041105  0.0006162438

$vcov[[375]]
              (Intercept)             x
(Intercept)  0.0003113484 -0.0004198742
x           -0.0004198742  0.0007227552

$vcov[[376]]
              (Intercept)             x
(Intercept)  0.0002446336 -0.0003614796
x           -0.0003614796  0.0006922459

$vcov[[377]]
              (Intercept)            x
(Intercept)  0.0002361255 -0.000361732
x           -0.0003617320  0.000723643

$vcov[[378]]
              (Intercept)             x
(Intercept)  0.0002072788 -0.0003326586
x           -0.0003326586  0.0007198519

$vcov[[379]]
              (Intercept)             x
(Intercept)  0.0002195704 -0.0003396193
x           -0.0003396193  0.0007287207

$vcov[[380]]
              (Intercept)             x
(Intercept)  0.0002071841 -0.0003221325
x           -0.0003221325  0.0006746254

$vcov[[381]]
              (Intercept)             x
(Intercept)  0.0001897457 -0.0003117189
x           -0.0003117189  0.0006996311

$vcov[[382]]
              (Intercept)             x
(Intercept)  0.0002124520 -0.0003042942
x           -0.0003042942  0.0006270534

$vcov[[383]]
              (Intercept)             x
(Intercept)  0.0002566315 -0.0003852144
x           -0.0003852144  0.0007282695

$vcov[[384]]
              (Intercept)             x
(Intercept)  0.0002303438 -0.0003653846
x           -0.0003653846  0.0007484708

$vcov[[385]]
              (Intercept)             x
(Intercept)  0.0002587283 -0.0003865455
x           -0.0003865455  0.0007204901

$vcov[[386]]
              (Intercept)             x
(Intercept)  0.0002820951 -0.0004067028
x           -0.0004067028  0.0007443693

$vcov[[387]]
              (Intercept)             x
(Intercept)  0.0002575249 -0.0003876421
x           -0.0003876421  0.0007301768

$vcov[[388]]
              (Intercept)             x
(Intercept)  0.0002316535 -0.0003745853
x           -0.0003745853  0.0008170400

$vcov[[389]]
              (Intercept)             x
(Intercept)  0.0002159920 -0.0003170288
x           -0.0003170288  0.0006582923

$vcov[[390]]
              (Intercept)             x
(Intercept)  0.0002492182 -0.0003754077
x           -0.0003754077  0.0007624302

$vcov[[391]]
              (Intercept)             x
(Intercept)  0.0002618621 -0.0003909597
x           -0.0003909597  0.0007944784

$vcov[[392]]
              (Intercept)             x
(Intercept)  0.0002357271 -0.0003574427
x           -0.0003574427  0.0007123152

$vcov[[393]]
              (Intercept)             x
(Intercept)  0.0002207077 -0.0003369749
x           -0.0003369749  0.0006870749

$vcov[[394]]
              (Intercept)             x
(Intercept)  0.0002425493 -0.0003594052
x           -0.0003594052  0.0007162400

$vcov[[395]]
              (Intercept)             x
(Intercept)  0.0002741028 -0.0003936794
x           -0.0003936794  0.0007558980

$vcov[[396]]
              (Intercept)             x
(Intercept)  0.0002174633 -0.0003098845
x           -0.0003098845  0.0005885996

$vcov[[397]]
              (Intercept)             x
(Intercept)  0.0002178007 -0.0003298878
x           -0.0003298878  0.0006740361

$vcov[[398]]
              (Intercept)             x
(Intercept)  0.0002325992 -0.0003399829
x           -0.0003399829  0.0006600179

$vcov[[399]]
              (Intercept)             x
(Intercept)  0.0002078348 -0.0003227412
x           -0.0003227412  0.0006564932

$vcov[[400]]
              (Intercept)             x
(Intercept)  0.0002620485 -0.0003692608
x           -0.0003692608  0.0006706149

$vcov[[401]]
              (Intercept)             x
(Intercept)  0.0002184364 -0.0003331237
x           -0.0003331237  0.0007045581

$vcov[[402]]
              (Intercept)             x
(Intercept)  0.0002287757 -0.0003422133
x           -0.0003422133  0.0006715824

$vcov[[403]]
              (Intercept)             x
(Intercept)  0.0001943997 -0.0003112327
x           -0.0003112327  0.0006606412

$vcov[[404]]
              (Intercept)             x
(Intercept)  0.0002302672 -0.0003529435
x           -0.0003529435  0.0007096418

$vcov[[405]]
              (Intercept)             x
(Intercept)  0.0002660500 -0.0003821907
x           -0.0003821907  0.0007228091

$vcov[[406]]
              (Intercept)             x
(Intercept)  0.0003119871 -0.0004400069
x           -0.0004400069  0.0007780697

$vcov[[407]]
              (Intercept)             x
(Intercept)  0.0002115263 -0.0003223655
x           -0.0003223655  0.0006579025

$vcov[[408]]
              (Intercept)             x
(Intercept)  0.0001969557 -0.0003038753
x           -0.0003038753  0.0006061209

$vcov[[409]]
              (Intercept)             x
(Intercept)  0.0002326910 -0.0003216099
x           -0.0003216099  0.0006032546

$vcov[[410]]
              (Intercept)             x
(Intercept)  0.0002187212 -0.0003217196
x           -0.0003217196  0.0006264235

$vcov[[411]]
              (Intercept)             x
(Intercept)  0.0002055143 -0.0003025523
x           -0.0003025523  0.0006060611

$vcov[[412]]
              (Intercept)             x
(Intercept)  0.0002025874 -0.0003053594
x           -0.0003053594  0.0006317147

$vcov[[413]]
              (Intercept)             x
(Intercept)  0.0003005361 -0.0004245018
x           -0.0004245018  0.0007352877

$vcov[[414]]
              (Intercept)             x
(Intercept)  0.0002353063 -0.0003582562
x           -0.0003582562  0.0007204393

$vcov[[415]]
              (Intercept)             x
(Intercept)  0.0002027706 -0.0003040509
x           -0.0003040509  0.0006027729

$vcov[[416]]
              (Intercept)             x
(Intercept)  0.0002361917 -0.0003317261
x           -0.0003317261  0.0006071049

$vcov[[417]]
              (Intercept)             x
(Intercept)  0.0002233026 -0.0003158683
x           -0.0003158683  0.0006147722

$vcov[[418]]
              (Intercept)             x
(Intercept)  0.0002206225 -0.0003304240
x           -0.0003304240  0.0006391433

$vcov[[419]]
              (Intercept)             x
(Intercept)  0.0001938448 -0.0002811511
x           -0.0002811511  0.0005628917

$vcov[[420]]
              (Intercept)             x
(Intercept)  0.0002541751 -0.0003917447
x           -0.0003917447  0.0007796127

$vcov[[421]]
              (Intercept)             x
(Intercept)  0.0001789370 -0.0002715845
x           -0.0002715845  0.0005905702

$vcov[[422]]
              (Intercept)             x
(Intercept)  0.0002036106 -0.0003039078
x           -0.0003039078  0.0006134293

$vcov[[423]]
              (Intercept)             x
(Intercept)  0.0002264930 -0.0003283964
x           -0.0003283964  0.0006384791

$vcov[[424]]
              (Intercept)             x
(Intercept)  0.0002305465 -0.0003449852
x           -0.0003449852  0.0006799623

$vcov[[425]]
              (Intercept)             x
(Intercept)  0.0002121130 -0.0003249942
x           -0.0003249942  0.0006467443

$vcov[[426]]
              (Intercept)             x
(Intercept)  0.0001994048 -0.0003009157
x           -0.0003009157  0.0006331612

$vcov[[427]]
              (Intercept)             x
(Intercept)  0.0002452493 -0.0003544886
x           -0.0003544886  0.0006780390

$vcov[[428]]
              (Intercept)             x
(Intercept)  0.0002341132 -0.0003480616
x           -0.0003480616  0.0006579762

$vcov[[429]]
              (Intercept)             x
(Intercept)  0.0002024254 -0.0003084024
x           -0.0003084024  0.0006561292

$vcov[[430]]
              (Intercept)             x
(Intercept)  0.0001909575 -0.0003089225
x           -0.0003089225  0.0006879594

$vcov[[431]]
              (Intercept)             x
(Intercept)  0.0002495316 -0.0003805874
x           -0.0003805874  0.0007815546

$vcov[[432]]
              (Intercept)             x
(Intercept)  0.0002571393 -0.0003740415
x           -0.0003740415  0.0006763573

$vcov[[433]]
              (Intercept)             x
(Intercept)  0.0002067493 -0.0003294023
x           -0.0003294023  0.0007147498

$vcov[[434]]
              (Intercept)             x
(Intercept)  0.0002870275 -0.0004305153
x           -0.0004305153  0.0008692587

$vcov[[435]]
              (Intercept)             x
(Intercept)  0.0001936847 -0.0002905905
x           -0.0002905905  0.0005934476

$vcov[[436]]
              (Intercept)             x
(Intercept)  0.0001269631 -0.0001885109
x           -0.0001885109  0.0003768984

$vcov[[437]]
              (Intercept)             x
(Intercept)  0.0002223616 -0.0003247020
x           -0.0003247020  0.0006294647

$vcov[[438]]
              (Intercept)             x
(Intercept)  0.0002292925 -0.0003589568
x           -0.0003589568  0.0007393253

$vcov[[439]]
              (Intercept)             x
(Intercept)  0.0001841753 -0.0002844396
x           -0.0002844396  0.0005761496

$vcov[[440]]
              (Intercept)             x
(Intercept)  0.0002002375 -0.0003105999
x           -0.0003105999  0.0006328221

$vcov[[441]]
              (Intercept)             x
(Intercept)  0.0002228916 -0.0003393547
x           -0.0003393547  0.0006985994

$vcov[[442]]
              (Intercept)             x
(Intercept)  0.0002305385 -0.0003492654
x           -0.0003492654  0.0006970479

$vcov[[443]]
              (Intercept)             x
(Intercept)  0.0002012718 -0.0003067735
x           -0.0003067735  0.0006779497

$vcov[[444]]
              (Intercept)             x
(Intercept)  0.0002263644 -0.0003380990
x           -0.0003380990  0.0006848969

$vcov[[445]]
              (Intercept)             x
(Intercept)  0.0002495402 -0.0003709652
x           -0.0003709652  0.0007130506

$vcov[[446]]
              (Intercept)             x
(Intercept)  0.0002040580 -0.0003024111
x           -0.0003024111  0.0006156315

$vcov[[447]]
              (Intercept)             x
(Intercept)  0.0002313398 -0.0003403708
x           -0.0003403708  0.0006768344

$vcov[[448]]
              (Intercept)             x
(Intercept)  0.0002628344 -0.0003901726
x           -0.0003901726  0.0007636650

$vcov[[449]]
              (Intercept)             x
(Intercept)  0.0002374043 -0.0003553257
x           -0.0003553257  0.0007264850

$vcov[[450]]
              (Intercept)             x
(Intercept)  0.0002577622 -0.0003773709
x           -0.0003773709  0.0007660970

$vcov[[451]]
              (Intercept)             x
(Intercept)  0.0001951805 -0.0003042165
x           -0.0003042165  0.0006398132

$vcov[[452]]
              (Intercept)             x
(Intercept)  0.0002277238 -0.0003375663
x           -0.0003375663  0.0006844174

$vcov[[453]]
              (Intercept)             x
(Intercept)  0.0002587649 -0.0003769840
x           -0.0003769840  0.0007433968

$vcov[[454]]
              (Intercept)             x
(Intercept)  0.0002734106 -0.0003870717
x           -0.0003870717  0.0007284970

$vcov[[455]]
              (Intercept)             x
(Intercept)  0.0002019914 -0.0003161633
x           -0.0003161633  0.0006853421

$vcov[[456]]
              (Intercept)             x
(Intercept)  0.0002374001 -0.0003450583
x           -0.0003450583  0.0006766674

$vcov[[457]]
              (Intercept)             x
(Intercept)  0.0002543128 -0.0003987869
x           -0.0003987869  0.0008602529

$vcov[[458]]
              (Intercept)             x
(Intercept)  0.0002258773 -0.0003569869
x           -0.0003569869  0.0007465080

$vcov[[459]]
              (Intercept)             x
(Intercept)  0.0002366540 -0.0003441812
x           -0.0003441812  0.0006647091

$vcov[[460]]
              (Intercept)             x
(Intercept)  0.0002035013 -0.0003185106
x           -0.0003185106  0.0006728174

$vcov[[461]]
              (Intercept)             x
(Intercept)  0.0002218515 -0.0003300805
x           -0.0003300805  0.0006715531

$vcov[[462]]
              (Intercept)             x
(Intercept)  0.0002380754 -0.0003571419
x           -0.0003571419  0.0006887302

$vcov[[463]]
              (Intercept)             x
(Intercept)  0.0002624198 -0.0003894131
x           -0.0003894131  0.0007682959

$vcov[[464]]
              (Intercept)             x
(Intercept)  0.0002197255 -0.0003335626
x           -0.0003335626  0.0006889783

$vcov[[465]]
              (Intercept)             x
(Intercept)  0.0002443082 -0.0003632190
x           -0.0003632190  0.0007201162

$vcov[[466]]
              (Intercept)             x
(Intercept)  0.0002387058 -0.0003564625
x           -0.0003564625  0.0006742334

$vcov[[467]]
              (Intercept)             x
(Intercept)  0.0002604429 -0.0003779215
x           -0.0003779215  0.0007377255

$vcov[[468]]
              (Intercept)             x
(Intercept)  0.0002403186 -0.0003708556
x           -0.0003708556  0.0007417527

$vcov[[469]]
              (Intercept)             x
(Intercept)  0.0002332533 -0.0003381550
x           -0.0003381550  0.0006506476

$vcov[[470]]
              (Intercept)             x
(Intercept)  0.0002596600 -0.0004086151
x           -0.0004086151  0.0008595212

$vcov[[471]]
              (Intercept)             x
(Intercept)  0.0002277268 -0.0003699862
x           -0.0003699862  0.0008002428

$vcov[[472]]
              (I...
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