1 Description

The dataset contains the results of a mathematics placement test for 200 freshmen entering Bowling Green State University. Form B of this test consists of 35 multiple-choice questions on topics in high school algebra.

Source: Johnson, V.E., & Albert, J.H. (1998). Ordinal Data Modeling. p. 212.

Column 1: Student ID
Columns 2-36: Score on questions 1-35, Correct = 1, Incorrect = 0
# load package

pacman::p_load(lattice, tidyverse, nlme, nlstools)

2 Input Data

dta4 <- read.table("C:/Users/HANK/Desktop/HOMEWORK/mathPlacement.asc", header = F)

names(dta4) <- c("ID", paste("a", 1:35, sep = ""))

str(dta4)
## 'data.frame':    200 obs. of  36 variables:
##  $ ID : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ a1 : int  0 1 1 1 1 1 0 0 1 0 ...
##  $ a2 : int  1 1 1 1 1 1 1 0 0 0 ...
##  $ a3 : int  1 1 1 1 1 1 0 0 1 1 ...
##  $ a4 : int  0 1 1 0 1 1 0 0 0 1 ...
##  $ a5 : int  1 1 1 1 1 1 1 0 1 0 ...
##  $ a6 : int  1 1 1 1 1 1 1 0 1 1 ...
##  $ a7 : int  1 1 1 1 1 1 1 0 1 1 ...
##  $ a8 : int  0 1 1 1 1 1 1 0 0 1 ...
##  $ a9 : int  0 1 1 1 1 1 0 0 1 1 ...
##  $ a10: int  1 1 1 1 1 0 1 0 0 1 ...
##  $ a11: int  1 1 1 1 1 1 1 0 1 0 ...
##  $ a12: int  1 1 1 1 0 1 0 0 1 1 ...
##  $ a13: int  1 0 1 1 1 1 1 0 1 0 ...
##  $ a14: int  1 1 1 1 1 1 0 1 0 1 ...
##  $ a15: int  1 1 1 0 0 1 1 0 0 1 ...
##  $ a16: int  0 0 1 0 0 1 0 0 0 1 ...
##  $ a17: int  0 1 1 0 1 1 1 0 1 0 ...
##  $ a18: int  1 1 1 1 1 1 1 0 1 0 ...
##  $ a19: int  1 1 1 0 0 1 1 0 0 0 ...
##  $ a20: int  1 1 1 1 1 1 1 0 0 1 ...
##  $ a21: int  1 1 0 0 0 0 0 0 0 0 ...
##  $ a22: int  1 0 1 1 0 0 0 0 1 1 ...
##  $ a23: int  1 1 1 1 1 1 1 0 0 0 ...
##  $ a24: int  1 1 1 0 1 0 1 0 0 0 ...
##  $ a25: int  1 1 1 1 0 1 1 1 0 0 ...
##  $ a26: int  1 1 1 1 0 1 0 1 0 1 ...
##  $ a27: int  0 1 1 0 0 1 1 0 1 1 ...
##  $ a28: int  0 1 1 0 0 1 1 0 0 0 ...
##  $ a29: int  0 0 1 1 1 1 0 0 0 0 ...
##  $ a30: int  1 1 1 1 0 1 1 0 1 1 ...
##  $ a31: int  1 1 1 1 1 1 0 0 0 0 ...
##  $ a32: int  0 0 1 1 0 1 1 0 0 0 ...
##  $ a33: int  1 0 1 1 0 0 1 0 0 0 ...
##  $ a34: int  1 1 0 0 1 0 1 0 0 1 ...
##  $ a35: int  1 1 1 1 1 1 1 0 0 0 ...
dta4 <- dta4 %>%
    mutate(total = rowSums(dta4[ ,2:36]))

ggplot(dta4, aes(ID, total))+
  geom_point()

p <- pnorm(dta4$a1, dta4$a2, dta4$a3, dta4$a35)
plot(p)

Model:
Pr{Yij = 1} = Φ(ajθi - bj),

where i is the subject index and j is the item index.