In this tutorial, we show that the alternate maximization (AM) is used in the first step of the two-step estimation method and the information criterion (IC) method is adopted to choose the number of factors.
The package can be loaded with the command:
First, we generate the data with homogeneous normal variables.
Then, we set the algorithm parameters and fit model
# Obtain the observed data
XList <- dat$XList # this is the data in the form of matrix list.
str(XList)
X <- dat$X # this is the data in form of matrix
# set variables' type, 'gaussian' means there is continous variable type.
types <- 'gaussian' Third, we fit the GFM model with user-specified number of factors.
# specify q=2
gfm1 <- gfm(XList, types, algorithm="AM", q=2, verbose = FALSE)
# measure the performance of GFM estimators in terms of canonical correlations
measurefun(gfm1$hH, dat$H0, type='ccor')
measurefun(gfm1$hB, dat$B0, type='ccor')The number of factors can also be determined by data-driven manners.
First, we generate the data with heterogeous normal variables and set the parameters of algorithm.
dat <- gendata(seed=1, n=100, p=100, type='heternorm', q=2, rho=1)
# Obtain the observed data
XList <- dat$XList # this is the data in the form of matrix list.
str(XList)
X <- dat$X # this is the data in form of matrix
# set variables' type, 'gaussian' means there is continous variable type.
types <- 'gaussian' Third, we fit the GFM model with user-specified number of factors and compare the results with that of linear factor models.
# specify q=2
gfm1 <- gfm(XList, types, algorithm="AM", q=2, verbose = FALSE)
# measure the performance of GFM estimators in terms of canonical correlations
corH_gfm <- measurefun(gfm1$hH, dat$H0, type='ccor')
corB_gfm <- measurefun(gfm1$hB, dat$B0, type='ccor')
lfm1 <- Factorm(X, q=2)
corH_lfm <- measurefun(lfm1$hH, dat$H0, type='ccor')
corB_lfm <- measurefun(lfm1$hB, dat$B0, type='ccor')
library(ggplot2)
df1 <- data.frame(CCor= c(corH_gfm, corH_lfm, corB_gfm, corB_lfm),
Method =factor(rep(c('GFM', "LFM"), times=2)),
Quantity= factor(c(rep('factors',2), rep("loadings", 2))))
ggplot(data=df1, aes(x=Quantity, y=CCor, fill=Method)) + geom_bar(position = "dodge", stat="identity",width = 0.5)The number of factors can also be determined by data-driven manners.
First, we generate the data with Count(Poisson) variables and set the parameters of algorithm.
q <- 3; p <- 200
dat <- gendata(seed=1, n=200, p=p, type='pois', q=q, rho=4)
# Obtain the observed data
XList <- dat$XList # this is the data in the form of matrix list.
str(XList)
X <- dat$X # this is the data in form of matrix
# set variables' type, 'gaussian' means there is continous variable type.
types <- 'poisson'Second, we we fit the GFM models given the true number of factors.
system.time(
hq <- chooseFacNumber(XList, types, q_set=1:6, select_method = "IC", parallelList=list(parallel=TRUE))
)Third, we compare the results with that of linear factor models.
# measure the performance of GFM estimators in terms of canonical correlations
corH_gfm <- measurefun(gfm1$hH, dat$H0, type='ccor')
corB_gfm <- measurefun(gfm1$hB, dat$B0, type='ccor')
lfm1 <- Factorm(X, q=3)
corH_lfm <- measurefun(lfm1$hH, dat$H0, type='ccor')
corB_lfm <- measurefun(lfm1$hB, dat$B0, type='ccor')
library(ggplot2)
df1 <- data.frame(CCor= c(corH_gfm, corH_lfm, corB_gfm, corB_lfm),
Method =factor(rep(c('GFM', "LFM"), times=2)),
Quantity= factor(c(rep('factors',2), rep("loadings", 2))))
ggplot(data=df1, aes(x=Quantity, y=CCor, fill=Method)) + geom_bar(position = "dodge", stat="identity",width = 0.5)First, we generate the data with Count(Poisson) variables and set the parameters of algorithm. Then fit the GFM model with user-specified number of factors.
dat <- gendata(seed=1, n=200, p=200, type='pois_bino', q=2, rho=2)
# Obtain the observed data
XList <- dat$XList # this is the data in the form of matrix list.
str(XList)
X <- dat$X # this is the data in form of matrix
# set variables' type, 'gaussian' means there is continous variable type.
types <- dat$types
table(dat$X[,1])
table(dat$X[, 200])
# user-specified q=2
gfm2 <- gfm(XList, types, algorithm="AM", q=2, verbose = FALSE)
measurefun(gfm2$hH, dat$H0, type='ccor')
measurefun(gfm2$hB, dat$B0, type='ccor')Third, we compare the results with that of linear factor models.
# select q automatically
hq <- chooseFacNumber(XList, types, select_method='IC', q_set = 1:4, verbose = FALSE, parallelList=list(parallel=TRUE))
# measure the performance of GFM estimators in terms of canonical correlations
corH_gfm <- measurefun(gfm2$hH, dat$H0, type='ccor')
corB_gfm <- measurefun(gfm2$hB, dat$B0, type='ccor')
Compare with linear factor models
lfm1 <- Factorm(dat$X, q=3)
corH_lfm <- measurefun(lfm1$hH, dat$H0, type='ccor')
corB_lfm <- measurefun(lfm1$hB, dat$B0, type='ccor')
library(ggplot2)
df1 <- data.frame(CCor= c(corH_gfm, corH_lfm, corB_gfm, corB_lfm),
Method =factor(rep(c('GFM', "LFM"), times=2)),
Quantity= factor(c(rep('factors',2), rep("loadings", 2))))
ggplot(data=df1, aes(x=Quantity, y=CCor, fill=Method)) + geom_bar(position = "dodge", stat="identity",width = 0.5)sessionInfo()
#> R version 4.1.2 (2021-11-01)
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