Minnesota High School Graduates

Description

Minnesota high school graduates of June 1930 were classified with respect to (a) Rank by thirds in their graduating class, (b) post-high school Status in April 1939 (4 levels), (c) Sex, (d) father's Occupational status (7 levels, from 1=High to 7=Low).

The data were first presented by Hoyt et al. (1959) and have been analyzed by Fienberg(1980), Plackett(1974) and others.

Usage

data(Hoyt)

Format

A 4-dimensional array resulting from cross-tabulating 4 variables for 13968 observations. The variable names and their levels are:

Details

Post high-school Status is natural to consider as the response. Rank and father's Occupation are ordinal variables.

Source

Fienberg, S. E. (1980). The Analysis of Cross-Classified Categorical Data. Cambridge, MA: MIT Press, p. 91-92.

R. L. Plackett, (1974). The Analysis of Categorical Data. London: Griffin.

References

Hoyt, C. J., Krishnaiah, P. R. and Torrance, E. P. (1959) Analysis of complex contingency tables, Journal of Experimental Education 27, 187-194.

See Also

minn38 provides the same data as a data frame.

Examples

data(Hoyt)

# display the table
structable(Status + Sex ~ Rank + Occupation, data=Hoyt)

# mosaic for independence model
plot(Hoyt, shade=TRUE)

# examine all pairwise mosaics
pairs(Hoyt, shade=TRUE)

# collapse Status to College vs. Non-College
Hoyt1 <- collapse.table(Hoyt, Status=c("College", rep("Non-College",3)))
plot(Hoyt1, shade=TRUE)

#################################################
# fitting models with loglm, plotting with mosaic
#################################################

# fit baseline log-linear model for Status as response
require(MASS)
hoyt.mod0 <- loglm(~ Status + (Sex*Rank*Occupation), 
  data=Hoyt1)
hoyt.mod0

mosaic(hoyt.mod0, 
  gp=shading_Friendly, 
  main="Baseline model: Status + (Sex*Rank*Occ)")

# add one-way association of Status with factors
hoyt.mod1 <- loglm(~ Status * (Sex + Rank + Occupation) + (Sex*Rank*Occupation), 
  data=Hoyt1)
hoyt.mod1

mosaic(hoyt.mod1, 
  gp=shading_Friendly, 
  main="Status * (Sex + Rank + Occ)")

# can we drop any terms?
drop1(hoyt.mod1, test="Chisq")

# assess model fit
anova(hoyt.mod0, hoyt.mod1)

# what terms to add?
add1(hoyt.mod1, ~.^2, test="Chisq")

# add interaction of Sex:Occupation on Status
hoyt.mod2 <- update(hoyt.mod1, ~ . + Status:Sex:Occupation)

mosaic(hoyt.mod2, 
  gp=shading_Friendly, 
  main="Adding Status:Sex:Occupation")

# compare model fits
anova(hoyt.mod0, hoyt.mod1, hoyt.mod2)

# Alternatively, try stepwise analysis, heading toward the saturated model
steps <- step(hoyt.mod0, 
  direction="forward", 
  scope=~Status*Sex*Rank*Occupation)

# display anova
steps$anova