# Edps 589
# c.j.anderson
#
# Log-linear models for square tables: Migration Data Example
#   o quasi-independence
#   o symmetry
#   o quasi-symmetry
#   o marginal homogeneity via a loglinear model
#
#
# On the data:
# If you want to get more up-to date trends see:
#https://www.census.gov/library/stories/2019/04/moves-from-south-west-dominate-recent-migration-flows.html
#  https://www.census.gov/data/tables/time-series/demo/geographic-mobility/state-to-state-migration.html
#
library(vcd)
library(vcdExtra)

def <- expand.grid(r1985=c("NorthEast","MidWest","South","West"),
                   r1980=c("NorthEast","MidWest","South","West"))
count <- c(11607,  100,  366,  124,
              87,13677,  515,  302,
			 172,  225,17819,  270,
			  63,  176,  286, 10192)
mig <- data.frame(def,count)
mig.tab<- xtabs(count ~ r1980 + r1985,data=mig)
# Check the data:
(addmargins(mig.tab))

# Finish set-up ....for now...
mig$r1980 <- as.factor(mig$r1980)
mig$r1985 <- as.factor(mig$r1985)

#
# Test of independence
#

summary(ind <- glm(count ~ r1980 + r1985, data=mig,family=poisson))
1-pchisq(ind$deviance,ind$df.residual)

#
# Quasi-Independence
#
# create factor for diagonal
mig$qi <- c(1,0,0,0,
            0,2,0,0,
		    0,0,3,0,
		    0,0,0,4)
mig$qi <- as.factor(mig$qi)	

summary(qi<- glm(count ~ r1980 + r1985 + qi,data=mig,family=poisson)
1-pchisq(qi$deviance,qi$df.residual)

#
# Symmetry
#
mig$symm <- c(1,  5 , 6,  7,
              5,  2,  8,  9,
			  6,  8,  3, 10,
			  7,  9, 10,  4)
mig$symm <- as.factor(mig$symm)

summary(symmetry <- glm(count~ symm,data=mig,family=poisson))
1-pchisq(symmetry$deviance,symmetry$df.residual)

#
# Quasi symmetry
#	
summary(quasi_sym <- glm(count~ r1980 + r1985+ symm,data=mig,family=poisson))
1-pchisq(quasi_sym$deviance,quasi_sym$df.residual)

#
# (indirect test) marginal homogeneity
#	
anova(symmetry,quasi_sym)
1 - pchisq(240,3)