cheating: GPA and chronic cheating (sample data)

Description Usage Format Source Examples

Description

Dichotomous responses by 319 undergraduates to four questions about cheating behavior, and each student's academic GPA.

Students responded either (1) no or (2) yes as to whether they had ever lied to avoid taking an exam (LIEEXAM), lied to avoid handing a term paper in on time (LIEPAPER), purchased a term paper to hand in as their own or had obtained a copy of an exam prior to taking the exam (FRAUD), or copied answers during an exam from someone sitting near to them (COPYEXAM).

The GPA variable is partitioned into five groups: (1) 2.99 or less; (2) 3.00-3.25; (3) 3.26-3.50; (4) 3.51-3.75; (5) 3.76-4.00.

This data set appears in Dayton (1998, pp. 33 and 85) as Tables 3.4 and 7.1.

Usage

1

Format

A data frame with 319 observations on 5 variables. Note: GPA data were not available for four students who reported never cheating.

Source

Dayton, C. Mitchell. 1998. Latent Class Scaling Analysis. Thousand Oaks, CA: SAGE Publications.

Examples

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##
## Replication of latent class models in Dayton (1998)
##
## Example 1. Two-class LCA. (Table 3.3, p. 32)
##
data(cheating)
f <- cbind(LIEEXAM,LIEPAPER,FRAUD,COPYEXAM)~1
ch2 <- poLCA(f,cheating,nclass=2)	# log-likelihood: -440.0271 

##
## Example 2. Two-class latent class regression using 
## GPA as a covariate to predict class membership as 
## "cheaters" vs. "non-cheaters".
## (Table 7.1, p. 85, and Figure 7.1, p. 86)
##
f2 <- cbind(LIEEXAM,LIEPAPER,FRAUD,COPYEXAM)~GPA
ch2c <- poLCA(f2,cheating,nclass=2)	# log-likelihood: -429.6384 
GPAmat <- cbind(1,c(1:5))
exb <- exp(GPAmat %*% ch2c$coeff)
matplot(c(1:5),cbind(1/(1+exb),exb/(1+exb)),type="l",lwd=2,
	main="GPA as a predictor of persistent cheating",
	xlab="GPA category, low to high",
	ylab="Probability of latent class membership")
text(1.7,0.3,"Cheaters")
text(1.7,0.7,"Non-cheaters")

##
## Compare results from Example 1 to Example 2.
## Non-simultaneous estimation of effect of GPA on latent class
## membership biases the estimated effect in Example 1. 
##
cheatcl <- which.min(ch2$P)
predcc <- sapply(c(1:5),function(v) mean(ch2$posterior[cheating$GPA==v,cheatcl],na.rm=TRUE))
## Having run Ex.2, add to plot:
matplot(c(1:5),cbind(1-predcc,predcc),type="l",lwd=2,add=TRUE)
text(4,0.14,"Cheaters\n (non-simul. estimate)")
text(4,0.87,"Non-cheaters\n (non-simul. estimate)")

Example output

Loading required package: scatterplot3d
Loading required package: MASS
Conditional item response (column) probabilities,
 by outcome variable, for each class (row) 
 
$LIEEXAM
           Pr(1)  Pr(2)
class 1:  0.4231 0.5769
class 2:  0.9834 0.0166

$LIEPAPER
           Pr(1)  Pr(2)
class 1:  0.4109 0.5891
class 2:  0.9708 0.0292

$FRAUD
           Pr(1)  Pr(2)
class 1:  0.7840 0.2160
class 2:  0.9629 0.0371

$COPYEXAM
           Pr(1)  Pr(2)
class 1:  0.6236 0.3764
class 2:  0.8181 0.1819

Estimated class population shares 
 0.1606 0.8394 
 
Predicted class memberships (by modal posterior prob.) 
 0.1693 0.8307 
 
========================================================= 
Fit for 2 latent classes: 
========================================================= 
number of observations: 319 
number of estimated parameters: 9 
residual degrees of freedom: 6 
maximum log-likelihood: -440.0271 
 
AIC(2): 898.0542
BIC(2): 931.9409
G^2(2): 7.764242 (Likelihood ratio/deviance statistic) 
X^2(2): 8.3234 (Chi-square goodness of fit) 
 
Conditional item response (column) probabilities,
 by outcome variable, for each class (row) 
 
$LIEEXAM
           Pr(1)  Pr(2)
class 1:  0.4389 0.5611
class 2:  0.9903 0.0097

$LIEPAPER
           Pr(1)  Pr(2)
class 1:  0.4858 0.5142
class 2:  0.9647 0.0353

$FRAUD
           Pr(1)  Pr(2)
class 1:  0.7850 0.2150
class 2:  0.9655 0.0345

$COPYEXAM
           Pr(1)  Pr(2)
class 1:  0.5925 0.4075
class 2:  0.8257 0.1743

Estimated class population shares 
 0.1781 0.8219 
 
Predicted class memberships (by modal posterior prob.) 
 0.1492 0.8508 
 
========================================================= 
Fit for 2 latent classes: 
========================================================= 
2 / 1 
            Coefficient  Std. error  t value  Pr(>|t|)
(Intercept)    -0.11342     0.50992   -0.222     0.833
GPA             0.84249     0.28132    2.995     0.030
========================================================= 
number of observations: 315 
number of estimated parameters: 10 
residual degrees of freedom: 5 
maximum log-likelihood: -429.6384 
 
AIC(2): 879.2768
BIC(2): 916.8025
X^2(2): 8.641712 (Chi-square goodness of fit) 
 

poLCA documentation built on May 29, 2017, 5:59 p.m.