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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:

• If the conditional mean $$\mathbb E (Y \vert X)$$ is not linear (“first order misspecification”), then the Ordinary Least Squares (OLS) regression coefficients $$\hat \beta$$ consistently estimate: $\beta \equiv \text{arg } \min _{\beta^\prime} \mathbb E((Y-X\beta^\prime)^2) (\#eq:target)$ which can be thought as the “best linear approximation of the response”3.

• Both non-linearity in the sense of the previous point, and $$X$$-dependence in $$\mathbb{V}(Y \vert X)$$ (“second order misspecification”) affect the sampling distribution of $$\hat \beta$$ and, in particular, $$\mathbb{V}(\hat \beta)$$, which is the relevant quantity for inference in the large-sample limit.

• Both problems can be efficiently addressed through the so-called “sandwich” estimators for the covariance matrix of $$\hat \beta$$ (White 1980), whose consistency is robust to both type of misspecification.

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 [343,] -0.1458178 0.9463383 [344,] -0.1617022 0.9958572 [345,] -0.1934703 1.0433425 [346,] -0.1747770 0.9896024 [347,] -0.1639795 0.9949930 [348,] -0.1678332 1.0100608 [349,] -0.1852163 1.0114238 [350,] -0.1538768 0.9834078 [351,] -0.1353845 0.9513650 [352,] -0.1491467 0.9798387 [353,] -0.1538934 0.9834331 [354,] -0.1590341 0.9853227 [355,] -0.1762377 1.0152540 [356,] -0.1724302 1.0212485 [357,] -0.1730765 1.0278204 [358,] -0.1762056 1.0251000 [359,] -0.1443106 0.9685429 [360,] -0.1838002 1.0060400 [361,] -0.1601542 1.0121024 [362,] -0.2006681 1.0544025 [363,] -0.1905956 1.0448073 [364,] -0.1746614 1.0028538 [365,] -0.1429341 0.9602030 [366,] -0.1332995 0.9410687 [367,] -0.1732458 1.0167090 [368,] -0.1772064 0.9966349 [369,] -0.1613933 1.0168273 [370,] -0.1598497 0.9825419 [371,] -0.1731645 0.9792333 [372,] -0.1589952 0.9875491 [373,] -0.1803699 1.0404335 [374,] -0.1639934 0.9774678 [375,] -0.1981938 1.0829926 [376,] -0.1848798 1.0278461 [377,] -0.1591529 0.9696276 [378,] -0.1540566 0.9576214 [379,] -0.1496030 0.9681593 [380,] -0.1526642 0.9656279 [381,] -0.1519919 0.9465051 [382,] -0.1467272 1.0010838 [383,] -0.1933998 1.0302383 [384,] -0.1750050 0.9874161 [385,] -0.1934355 1.0295133 [386,] -0.1767963 1.0162017 [387,] -0.1655212 0.9774993 [388,] -0.1602204 0.9702900 [389,] -0.1629489 1.0188029 [390,] -0.1471399 0.9608970 [391,] -0.1516947 0.9795651 [392,] -0.1647744 0.9839899 [393,] -0.1403844 0.9421832 [394,] -0.1455642 0.9658617 [395,] -0.1644257 1.0115619 [396,] -0.1776377 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[789,] -0.1669974 1.0119140 [790,] -0.1636053 0.9902988 [791,] -0.1381472 0.9763245 [792,] -0.1711231 1.0071661 [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...