How can I run logistic regression loop that will run across all Independent variables , pairs and trios

Question

I would like to run the dependent variable of a logistic regression (in my data set it's : dat$admit) with all available variables, pairs and trios(3 Independent vars), each regression with a different Independent variables vs dependent variable. The outcome that I would like to get back is a list of each regression summary in a row: coeff,p-value ,AUC,CI 95%. Using the data set submitted below there should be 7 regressions:

dat$admit vs dat$female
dat$admit vs dat$apcalc
dat$admit vs dat$num
dat$admit vs dat$female + dat$apcalc
dat$admit vs dat$female + dat$num
dat$admit vs dat$apcalc + dat$num
dat$admit vs dat$female + dat$apcalc + dat$num

Here is a sample data set (where dat$admit is the logistic regression dependent variable) :

dat <- read.table(text = " female  apcalc    admit       num
0        0        0         7
0        0        1         1
0        1        0         3
0        1        1         7
1        0        0         5
1        0        1         1
1        1        0         0
1        1        1         6",header = TRUE)

Per @marek comment, the output should be like this (for female alone and from female & apcalc ): # Intercept Estimate P-Value (Intercept) P-Value (Estimate) AUC # female 0.000000e+00 0.000000e+00 1 1 0.5

female+apcalc 0.000000e+00 0.000000e+00 1 1 0.5

There is a good code that @David Arenburg wrote that produces the stats but with no models creations of pairs and trios so I would like to know how can add the models creations. Here is David Arenburg's code?

library(caTools)
ResFunc <- function(x) {
  temp <- glm(reformulate(x,response="admit"), data=dat,family=binomial)
  c(summary(temp)$coefficients[,1], 
    summary(temp)$coefficients[,4],
    colAUC(predict(temp, type = "response"), dat$admit))
}

temp <- as.data.frame(t(sapply(setdiff(names(dat),"admit"), ResFunc)))
colnames(temp) <- c("Intercept", "Estimate", "P-Value (Intercept)", "P-Value (Estimate)", "AUC")
temp

#          Intercept      Estimate P-Value (Intercept) P-Value (Estimate) AUC
# female 0.000000e+00  0.000000e+00                   1                  1 0.5
# apcalc 0.000000e+00  0.000000e+00                   1                  1 0.5
# num    5.177403e-16 -1.171295e-16                   1                  1 0.5

Any idea how to create this list? Thanks, Ron

Answer 1

Simple solution is to make the list of models by hand:

results <- list(
    "female"           = glm(admit~female         , family=binomial, dat)
    ,"apcalc"          = glm(admit~apcalc         , family=binomial, dat)
    ,"num"             = glm(admit~num            , family=binomial, dat)
    ,"female + apcalc" = glm(admit~female + apcalc, family=binomial, dat)
    ,"female + num"    = glm(admit~female + num   , family=binomial, dat)
    ,"apcalc + num"    = glm(admit~apcalc + num   , family=binomial, dat)
    ,"all"             = glm(admit~female + apcalc + num, family=binomial, dat)
)

Then you could check models by lapplying over the list of models:

lapply(results, summary)

Or more advanced (coefficient statistics):

require(plyr)
ldply(results, function(m) {
    name_rows(as.data.frame(summary(m)$coefficients))
})

In similar way you could extract every information you want. Just write function to extract statistics you want, which takes glm model as argument:

get_everything_i_want <- function(model) {
    #... do what i want ...
    # eg:
    list(AIC = AIC(model))
}

and then apply to each model:

lapply(results, get_everything_i_want)
# $female
# $female$AIC
# [1] 15.0904
# $apcalc
# $apcalc$AIC
# [1] 15.0904
# $num
# $num$AIC
# [1] 15.0904
# $`female + apcalc`
# $`female + apcalc`$AIC
# [1] 17.0904
# $`female + num`
# $`female + num`$AIC
# [1] 17.0904
# $`apcalc + num`
# $`apcalc + num`$AIC
# [1] 17.0904
# $all
# $all$AIC
# [1] 19.0904