catspec (version 0.93)

sqtab: sqtab: models for square tables

Description

These functions are used to estimate loglinear models for square tables such as quasi-independence, quasi-symmetry.

Usage

mob.qi(rowvar, colvar, constrained = FALSE, print.labels = FALSE)
mob.eqmain(rowvar, colvar, print.labels = FALSE)
mob.symint(rowvar, colvar, print.labels = FALSE)
mob.cp(rowvar,colvar)
mob.unif(rowvar, colvar)
mob.rc1(rowvar, colvar, equal = FALSE, print.labels = FALSE)
fitmacro(object)
check.square(rowvar, colvar, equal = TRUE)

Arguments

rowvar

Factor representing the row variable

colvar

Factor representing the column variable

print.labels

If FALSE (default) then numeric values rather than factor values are printed for compact results

equal

(mob.rc1) If TRUE, a homogeneous row and column effects model 1 with equal scale values for the row and column variables is estimated. Otherwise, a (regular) RC1 model is estimated with different scale values for the row and column

constrained

(mob.qi)If TRUE, a quasi-independence model-constrained is estimated with a single parameter for the diagonal cells

object

(fitmacro) An object of class glm for family=poisson and link=log

Value

• mob.qi
  A factor that will produce coefficients for the diagonal cells of a table, using off- diagonal cells as base category
• mob.eqmain
  A design matrix with equality contraints on the main effects
• mob.symint
  A design matrix for an interaction with equality contraints on coefficients on opposite sides of the diagonal
• mob.cp
  A set of vectors for a crossings-parameter model
• mob.unif
  A vector for a uniform association model
• mob.rc1
  A set of vectors for a row and columns model 1
• fitmacro
  Prints deviance, df, BIC, AIC, number of parameters and N
• check.square
  Stops function if either the row or column variable is not a factor or if the number of levels is unequal

Details

These functions are used to estimate loglinear models for square tables: mob.qi{Quasi-independence} mob.eqmain{Equal main effects (Hope's halfway model)} mob.symint{Symmetric interaction} mob.cp{Crossings-parameter model} mob.unif{Uniform association} mob.rc1{Row and columns model 1} fitmacro{Calculates BIC and AIC relative to a saturated loglinear model} check.square{Internal function to check if row and column variables are both factors with the same number of levels}

References

Hout, Michael. (1983). Mobility Tables. Sage Publication 07-031. Goodman, Leo A. (1984). The analysis of cross-classified data having ordered categories. Cambridge, Mass.: Harvard University Press.

See Also

glm, mclgen

Examples

# Examples of loglinear models for square tables,
# from Hout, M. (1983). "Mobility Tables". Sage Publication 07-031

# Table from page 11 of "Mobility Tables"
# Original source: Featherman D.L., R.M. Hauser. (1978) "Opportunity and Change."
# New York: Academic, page 49

data(FHtab)
FHtab<-as.data.frame(FHtab)
attach(FHtab)

xtabs(Freq ~ .,FHtab)

# independence model
indep<-glm(Freq~OccFather+OccSon,family=poisson())
summary(indep)
fitmacro(indep)

wt <- as.numeric(OccFather != OccSon)
qi0<-glm(Freq~OccFather+OccSon,weights=wt,family=poisson())
# A quasi-independence loglinear model, using structural zeros
# (page 23 of "Mobility Tables").
#  0  1  1  1  1   values of variable "wt"
#  1  0  1  1  1
#  1  1  0  1  1
#  1  1  1  0  1
#  1  1  1  1  0
qi0<-glm(Freq~OccFather+OccSon,weights=wt,family=poisson())
summary(qi0)
fitmacro(qi0)

# Quasi-independence using a "dummy factor" to create the design
# vectors for the diagonal cells (page 23).
#  1  0  0  0  0
#  0  2  0  0  0
#  0  0  3  0  0
#  0  0  0  4  0
#  0  0  0  0  5
glm.qi<-glm(Freq~OccFather+OccSon+mob.qi(OccFather,OccSon),family=poisson())
summary(glm.qi)
fitmacro(glm.qi)

# Quasi-independence constrained (QPM-C, page 31)
# Single immobility parameter
#  1  0  0  0  0
#  0  1  0  0  0
#  0  0  1  0  0
#  0  0  0  1  0
#  0  0  0  0  1
glm.q0<-glm(Freq~OccFather+OccSon+mob.qi(OccFather,OccSon,constrained=TRUE),family=poisson())
# slightly different results than Hout also found in Stata: L2=2567.658, q0=0.964
summary(glm.q0)
fitmacro(glm.q0)

# Quasi-symmetry using the symmetric cross-classification (page 23)
#  0  1  2  3  4   values of variable "sym"
#  1  0  5  6  7
#  2  5  0  8  9
#  3  6  8  0 10
#  4  7  9 10  0  */
glm.qsym<-
glm(Freq~OccFather+OccSon+mob.symint(OccFather,OccSon),family=poisson())
summary(glm.qsym)
fitmacro(glm.qsym)

symmetry<-glm(Freq~mob.eqmain(OccFather,OccSon)
+mob.symint(OccFather,OccSon),family=poisson())
summary(symmetry)
fitmacro(symmetry)

# Crossings parameter model (page 35)
#  0  v1 v1 v1 v1 |  0  0  v2 v2 v2 |  0  0  0  v3 v3 |  0  0  0  0 v4
#  v1 0  0  0  0  |  0  0  v2 v2 v2 |  0  0  0  v3 v3 |  0  0  0  0 v4
#  v1 0  0  0  0  |  v2 v2 0  0  0  |  0  0  0  v3 v3 |  0  0  0  0 v4
#  v1 0  0  0  0  |  v2 v2 0  0  0  |  v3 v3 v3 0  0  |  0  0  0  0 v4
#  v1 0  0  0  0  |  v2 v2 0  0  0  |  v3 v3 v3 0  0  |  v4 v4 v4 v4 0
glm.cp<-glm(Freq~OccFather+OccSon+mob.cp(OccFather,OccSon),family=poisson())
summary(glm.cp)
fitmacro(glm.cp)

# Uniform association model: linear by linear association (page 58)
glm.unif<-glm(Freq~OccFather+OccSon+mob.unif(OccFather,OccSon),family=poisson())
summary(glm.unif)
fitmacro(glm.unif)

# RC model 1 (unequal row and column effects, page 58)
# Fits a uniform association parameter and row and column effect
# parameters. Row and column effect parameters have the
# restriction that the first and last categories are zero.
glm.rc1<-glm(Freq~OccFather+OccSon+mob.rc1(OccFather,OccSon),family=poisson())
summary(glm.rc1)
fitmacro(glm.rc1)

# Homogeneous row and column effects model 1 (page 58)
# An equality restriction is placed on the row and column effects
glm.hrc1<-glm(Freq~OccFather+OccSon+mob.rc1(OccFather,OccSon,equal=TRUE),family=poisson())
# Results differ from those in Hout, replicated by other programs
summary(glm.hrc1)
fitmacro(glm.hrc1)