# ILSE: a simple NHANES example

#### 2022-01-31

First, we load the ‘ILSE’ package and the real data which can be loaded by following command.

library("ILSE")
data("nhanes")

### Fit linear regression model

We fit the linear regression model using ‘ILSE’ function, and then compare with CC method and FIML method.

ncomp <- sum(complete.cases(nhanes))
message("Number of complete cases is ", ncomp, '\n')
ilse2 <- ilse(age~., data=nhanes, verbose=T)
print(ilse2)

Next, Bootstrap is applied to evaluate the standard error and p-values of each coefficients estimated by ILSE. We observe four significant coefficients.

set.seed(1)
s2 <- summary(ilse2, Nbt=20)
s2

### Compare with CC and FIML

First, we conduct CC analysis.

lm1 <- lm(age~., data=nhanes)
s_cc <- summary.lm(lm1)
s_cc

We fit linear regression model using FIML method.

fimllm <- fimlreg(age~., data=nhanes)
print(fimllm)

We also use bootstrap to evaluate the standard error and p-values of each coefficients estimated by ILSE. We observe only one significant coefficients.

s_fiml <- summary(fimllm, Nbt=20)
s_fiml

### Visualization

We visualize the p-vaules of each methods, where red line denotes 0.05 in y-axis and blue line 0.1 in y-axis.

library(ggplot2)
library(ggthemes)
pMat <- cbind(CC=s_cc\$coefficients[,4], ILSE=s2[,4], FIML=s_fiml[,4])
df1 <- data.frame(Pval= as.vector(pMat[-1,]),
Method =factor(rep(c('CC', "ILSE", "FIML"),each=3)),
covariate= factor(rep(row.names(pMat[-1,]), times=3)))
ggplot(data=df1, aes(x=covariate, y=Pval, fill=Method)) + geom_bar(position = "dodge", stat="identity",width = 0.5) + geom_hline(yintercept = 0.05, color='red') + geom_hline(yintercept = 0.1, color='blue') +
scale_fill_economist()

## Session information

sessionInfo()
#> R version 4.0.3 (2020-10-10)
#> Platform: x86_64-w64-mingw32/x64 (64-bit)
#> Running under: Windows 10 x64 (build 22000)
#>
#> Matrix products: default
#>
#> locale:
#>  LC_COLLATE=C
#>  LC_CTYPE=Chinese (Simplified)_China.936
#>  LC_MONETARY=Chinese (Simplified)_China.936
#>  LC_NUMERIC=C
#>  LC_TIME=Chinese (Simplified)_China.936
#>
#> attached base packages:
#>  stats     graphics  grDevices utils     datasets  methods   base
#>
#> loaded via a namespace (and not attached):
#>   digest_0.6.28   R6_2.5.1        jsonlite_1.7.2  magrittr_2.0.1
#>   evaluate_0.14   rlang_0.4.11    stringi_1.7.5   jquerylib_0.1.4
#>   bslib_0.3.1     rmarkdown_2.11  tools_4.0.3     stringr_1.4.0
#>  xfun_0.29       yaml_2.2.2      fastmap_1.1.0   compiler_4.0.3
#>  htmltools_0.5.2 knitr_1.37      sass_0.4.0