vcdExtra (version 0.8-5)

Hoyt: 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:

No	Name	Levels
1	Status	"College", "School", "Job", "Other"
2	Rank	"Low", "Middle", "High"
3	Occupation	"1", "2", "3", "4", "5", "6", "7"
4	Sex	"Male", "Female"

Details

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

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