Flexible Beta Modeling

October 27, 2014
By

(This article was first published on Yet Another Blog in Statistical Computing » S+/R, and kindly contributed to R-bloggers)

library(betareg)
library(sas7bdat)

df1 <- read.sas7bdat('lgd.sas7bdat')
df2 <- df1[df1$y < 1, ]

fml <- as.formula('y ~ x2 + x3 + x4 + x5 + x6 | x3 + x4 | x1 + x2')

### LATENT-CLASS BETA REGRESSION: AIC = -565 ###
mdl1 <- betamix(fml, data = df2, k = 2, FLXcontrol = list(iter.max = 500, minprior = 0.1))
print(mdl1)
#betamix(formula = fml, data = df2, k = 2, FLXcontrol = list(iter.max = 500, 
#    minprior = 0.1))
#
#Cluster sizes:
#  1   2 
#157 959 

summary(mdl1, which = 'concomitant')
#            Estimate Std. Error z value Pr(>|z|)   
#(Intercept) -1.35153    0.41988 -3.2188 0.001287 **
#x1           2.92537    1.13046  2.5878 0.009660 **
#x2           2.82809    1.42139  1.9897 0.046628 * 

summary(mdl1)
#$Comp.1$mean
#              Estimate Std. Error z value  Pr(>|z|)    
#(Intercept) -0.8963228  1.0385545 -0.8630 0.3881108    
#x2           3.1769062  0.6582108  4.8266 1.389e-06 ***
#x3          -0.0520060  0.0743714 -0.6993 0.4843805    
#x4           4.9642998  1.4204071  3.4950 0.0004741 ***
#x5           0.0021647  0.0022659  0.9554 0.3393987    
#x6           0.0248573  0.0062982  3.9467 7.922e-05 ***
#
#$Comp.1$precision
#            Estimate Std. Error z value  Pr(>|z|)    
#(Intercept) -5.37817    1.44817 -3.7138 0.0002042 ***
#x3           0.45009    0.10094  4.4589 8.239e-06 ***
#x4           3.06969    1.41450  2.1702 0.0299948 *  
#
#$Comp.2
#$Comp.2$mean
#              Estimate Std. Error z value  Pr(>|z|)    
#(Intercept) -1.8737088  0.3888454 -4.8186 1.445e-06 ***
#x2          -0.6318086  0.1892501 -3.3385 0.0008424 ***
#x3           0.1786425  0.0265428  6.7303 1.693e-11 ***
#x4           2.0646272  0.5256002  3.9281 8.561e-05 ***
#x5          -0.0064821  0.0014053 -4.6127 3.974e-06 ***
#x6           0.0018828  0.0022873  0.8231 0.4104318    
#
#$Comp.2$precision
#            Estimate Std. Error z value Pr(>|z|)   
#(Intercept) 1.092403   0.616974  1.7706 0.076630 . 
#x3          0.017330   0.040024  0.4330 0.665029   
#x4          2.138812   0.717702  2.9801 0.002882 **


### BETA REGRESSION TREE: AIC = -578 ###
mdl2 <- betatree(fml, data = df2, minsplit = 100)
print(mdl2)
#1) x2 <= 0.08584895; criterion = 1, statistic = 154.716
#  2)*  weights = 121 
#Terminal node model
#betaReg fit with coefficients:
#      (Intercept)                 x2                 x3                 x4  
#         3.307359          -2.854351          -0.262815          -2.414481  
#               x5                 x6  (phi)_(Intercept)           (phi)_x3  
#        -0.007555           0.030346           1.003767          -0.002907  
#         (phi)_x4  
#         2.528602  
#
#1) x2 > 0.08584895
#  3)*  weights = 995 
#Terminal node model
#betaReg fit with coefficients:
#      (Intercept)                 x2                 x3                 x4  
#        -2.134931          -0.194830           0.168136           2.811077  
#               x5                 x6  (phi)_(Intercept)           (phi)_x3  
#        -0.002070           0.004677          -1.018102           0.151778  
#         (phi)_x4  
#         2.142995  

sctest(mdl2, node = 1)
#                x1       x2
#statistic 113.4781 154.7165
#p.value     0.0000   0.0000

summary(mdl2)
#$`2`
#
#Coefficients (mean model with logit link):
#             Estimate Std. Error z value Pr(>|z|)    
#(Intercept)  3.307359   1.091289   3.031 0.002440 ** 
#x2          -2.854351   3.644882  -0.783 0.433561    
#x3          -0.262815   0.074716  -3.518 0.000436 ***
#x4          -2.414481   1.785447  -1.352 0.176276    
#x5          -0.007555   0.002788  -2.710 0.006738 ** 
#x6           0.030346   0.006833   4.441 8.96e-06 ***
#
#Phi coefficients (precision model with log link):
#             Estimate Std. Error z value Pr(>|z|)
#(Intercept)  1.003767   1.353496   0.742    0.458
#x3          -0.002907   0.090816  -0.032    0.974
#x4           2.528602   2.344241   1.079    0.281

#$`3`
#
#Coefficients (mean model with logit link):
#             Estimate Std. Error z value Pr(>|z|)    
#(Intercept) -2.134931   0.337784  -6.320 2.61e-10 ***
#x2          -0.194830   0.144062  -1.352  0.17625    
#x3           0.168136   0.022521   7.466 8.28e-14 ***
#x4           2.811077   0.387788   7.249 4.20e-13 ***
#x5          -0.002070   0.001136  -1.822  0.06848 .  
#x6           0.004677   0.001770   2.643  0.00822 ** 
#
#Phi coefficients (precision model with log link):
#            Estimate Std. Error z value Pr(>|z|)    
#(Intercept) -1.01810    0.46575  -2.186 0.028821 *  
#x3           0.15178    0.03057   4.965 6.88e-07 ***
#x4           2.14300    0.56979   3.761 0.000169 ***

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