GFM: installation and simulated example

Generate data with homogeneous normal variables

First, we generate the data with homogeneous normal variables.

## Homogeneous  normal variables
  dat <- gendata(q = 2, n=100, p=100, rho=3)

Then, we set the algorithm parameters and fit model

# full-one vector means there is only one variable type within all variables.
  group <- rep(1,ncol(dat$X)) 
# set variables' type, 'gaussian' means there is  continous variable type.
  type <- 'gaussian' 

Third, we fit the GFM model with user-specified number of factors.

# specify q=2
  gfm1 <- gfm(dat$X, group, type, q=2, output = 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.

# select q automatically
  gfm2 <- gfm(dat$X, group, type, q=NULL, q_set = 1:6, output = FALSE)
# measure the performance of GFM estimators in terms of canonical correlations
  measurefun(gfm2$hH, dat$H0, type='ccor')
  measurefun(gfm2$hB, dat$B0, type='ccor')

Generate data with heterogeous normal variables

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)
  group <- rep(1,ncol(dat$X))
  type <- '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(dat$X, group, type, q=2, output = 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(dat$X, q=2)
  corH_lfm <- measurefun(lfm1$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.

# select q automatically
  gfm2 <- gfm(dat$X, group, type, q=NULL, q_set = 1:4, output = FALSE)
# measure the performance of GFM estimators in terms of canonical correlations
  corH_gfm <- measurefun(gfm2$hH, dat$H0, type='ccor')
  corB_gfm <- measurefun(gfm2$hB, dat$B0, type='ccor')
  
  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)

Generate data with Count(Poisson) variables

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)
  group <- rep(1,ncol(dat$X))
  type <- 'poisson'

Second, we we fit the GFM models in the parallel manner.

  system.time(
    gfm2 <- gfm(dat$X, group, type,parallel = TRUE, q=NULL, q_set = 1:4, output = FALSE, fast_version = 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(gfm2$hH, dat$H0, type='ccor')
  corB_gfm <- measurefun(gfm2$hB, dat$B0, type='ccor')
  
  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)

Generate data with the mixed-types of Poisson and Binomial variables

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)
  group <- c(rep(1,ncol(dat$X)/2), rep(2,ncol(dat$X)/2))
  type <- c('poisson','binomial')
  table(dat$X[,1])
  table(dat$X[, 200])
  # user-specified q=2
  gfm2 <- gfm(dat$X, group, type, dropout = 2, q=2, output = FALSE, maxIter=5)
  measurefun(gfm2$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
  gfm2 <- gfm(dat$X, group, type, dropout = 2, q=NULL, q_set = 1:4, output = FALSE)
  # measure the performance of GFM estimators in terms of canonical correlations
  corH_gfm <- measurefun(gfm2$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)