Two-Stage Path Analysis (2S-PA) Model Examples

The example is from https://lavaan.ugent.be/tutorial/sem.html.

Load packages

library(lavaan)
library(R2spa)

Single group, single predictor¹

model <- ' 
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a*y2 + b*y3 + c*y4

  # regressions
    dem60 ~ ind60
'

To call tspa(), a data frame of factor scores is needed for all latent variables. To get this data frame, apply get_fs() to all latent variables and specify model parameter as their respective definitions. Combine factor scores for all latent variable using cbind() so that it can be used in tspa() for model building.

fs_dat_ind60 <- get_fs(data = PoliticalDemocracy, 
                       model = "ind60 =~ x1 + x2 + x3")
fs_dat_dem60 <- get_fs(data = PoliticalDemocracy, 
                       model = "dem60 =~ y1 + y2 + y3 + y4")
fs_dat <- cbind(fs_dat_ind60, fs_dat_dem60)

To build a Two-Stage Path Analysis model, simply call the tspa() function with model = regressions, data = The combined factor score data frame using get_fs(), and specify standard error as either a list or a data frame. Values for standard error can be found at column named fs_[variable name]_se. For example, the standard error of latent variable ind60 can be found at column fs_ind60_se in the fs_dat data frame.

tspa_fit <- tspa(model = "dem60 ~ ind60", 
                 data = fs_dat, 
                 se_fs = list(ind60 = 0.1213615, dem60 = 0.6756472))

To view the Two-Stage Path Analysis model, use attributes([model name])$tspaModel. Function cat() can help tidy up the model output. In the output, the values of error constraints are computed by squaring standard errors from the previous section.

cat(attributes(tspa_fit)$tspaModel)

## # latent variables (indicated by factor scores)
## ind60=~ c(1) * fs_ind60
## dem60=~ c(1) * fs_dem60
## 
## # constrain the errors
## fs_ind60~~ c(0.01472861368225) * fs_ind60
## fs_dem60~~ c(0.45649913886784) * fs_dem60
## 
## # structural model
## dem60 ~ ind60

Single group, multiple predictors

model <- ' 
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + y2 + y3 + y4
     dem65 =~ y5 + y6 + y7 + y8

  # regressions
    dem60 ~ ind60
    dem65 ~ ind60 + dem60

  # # residual correlations
  #   y1 ~~ y5
  #   y2 ~~ y4 + y6
  #   y3 ~~ y7
  #   y4 ~~ y8
  #   y6 ~~ y8
'

To call tspa(), a data frame of factor scores is needed for all latent variables. To get this data frame, apply get_fs() to all latent variables and specify model parameters as their respective definitions. Combine factor scores for all latent variables using cbind() to call tspa() for model building.

fs_dat_ind60 <- get_fs(data = PoliticalDemocracy, 
                       model = "ind60 =~ x1 + x2 + x3")
fs_dat_dem60 <- get_fs(data = PoliticalDemocracy, 
                       model = "dem60 =~ y1 + y2 + y3 + y4")
fs_dat_dem65 <- get_fs(data = PoliticalDemocracy, 
                       model = "dem65 =~ y5 + y6 + y7 + y8")
fs_dat <- cbind(fs_dat_ind60, fs_dat_dem60, fs_dat_dem65)

To build a Two-Stage Path Analysis model, simply call the tspa() function with model = regressions (for all predictors), data = the factor score data frame created by combining results from get_fs(), and specify standard errors as either a list or a data frame. Values for standard errors can be found at column named fs_[variable name]_se.² For example, the standard error of latent variable ind60 can be found at column fs_ind60_se in the fs_dat data frame. In the output model, the values of error constraints are computed by squaring standard errors.

tspa_3var_fit <- tspa(model = "dem60 ~ ind60
                          dem65 ~ ind60 + dem60", 
                      data = fs_dat, 
                      se_fs = list(ind60 = 0.1213615, dem60 = 0.6756472, 
                                   dem65 = 0.5724405))
cat(attributes(tspa_3var_fit)$tspaModel)

## # latent variables (indicated by factor scores)
## ind60=~ c(1) * fs_ind60
## dem60=~ c(1) * fs_dem60
## dem65=~ c(1) * fs_dem65
## 
## # constrain the errors
## fs_ind60~~ c(0.01472861368225) * fs_ind60
## fs_dem60~~ c(0.45649913886784) * fs_dem60
## fs_dem65~~ c(0.32768812604025) * fs_dem65
## 
## # structural model
## dem60 ~ ind60
##                           dem65 ~ ind60 + dem60

Multigroup, single predictor

model <- ' 
  # latent variable definitions
    visual =~ x1 + x2 + x3
    speed =~ x7 + x8 + x9

  # regressions
    visual ~ speed
'

To call tspa(), a data frame of factor scores is needed for all multigroup variables. To get this data frame, apply get_fs() to all multigroup variables and specify model parameter as their respective definitions. Combine factor scores for all multigroup variables using cbind() so that it can be fed in tspa() for model building.

hs_mod <- '
visual =~ x1 + x2 + x3
speed =~ x7 + x8 + x9
'

# get factor scores
fs_dat_visual <- get_fs(data = HolzingerSwineford1939, 
                        model = "visual =~ x1 + x2 + x3", 
                        group = "school")
fs_dat_speed <- get_fs(data = HolzingerSwineford1939, 
                       model = "speed =~ x7 + x8 + x9", 
                       group = "school")
fs_hs <- cbind(do.call(rbind, fs_dat_visual),
               do.call(rbind, fs_dat_speed))

To build a Two-Stage Path Analysis model, simply call the tspa() function with model = regression relation. Specify standard error as either a list or a data frame. Values for standard error can be found at column named fs_[variable name]_se. For example, the standard error of the multigroup variable visual can be found at column fs_visual_se in the fs_hs data frame. To get the standard errors for each group faster, unique() can be called upon the standard error column. For example, in this case, unique(fs_hs$fs_visual_se) can be called to get the standard errors for multigroup variable visual.

Function standardizedsolution() enables user to view a table of standard error, z score, p-value, and lower bound of confidence interval for each multigroup regression relation.

# tspa model
tspa_fit <- tspa(model = "visual ~ speed",
                 data = fs_hs,
                 se_fs = data.frame(visual = c(0.3391326, 0.311828),
                                    speed = c(0.2786875, 0.2740507)),
                 group = "school"
                 # group.equal = "regressions"
                 )
stdsol <- standardizedsolution(tspa_fit)
subset(stdsol, subset = op == "~")

##       lhs op   rhs group est.std    se     z pvalue ci.lower ci.upper
## 5  visual  ~ speed     1   0.277 0.114 2.423  0.015    0.053    0.501
## 16 visual  ~ speed     2   0.439 0.095 4.627  0.000    0.253    0.625

To view the Two-Stage Path Analysis model for multigroup, use attributes([model name])$tspaModel. Function cat() can help tidy up the model output. In the output, the values of error constraints are computed by squaring standard errors from the previous section.

cat(attributes(tspa_fit)$tspaModel)

## # latent variables (indicated by factor scores)
## visual=~ c(1, 1) * fs_visual
## speed=~ c(1, 1) * fs_speed
## 
## # constrain the errors
## fs_visual~~ c(0.11501092038276, 0.097236701584) * fs_visual
## fs_speed~~ c(0.07766672265625, 0.07510378617049) * fs_speed
## 
## # structural model
## visual ~ speed

Yixiao Li

2024-09-06

Single group, single predictor¹

Single group, multiple predictors

Multigroup, single predictor

Two-Stage Path Analysis (2S-PA) Model Examples

Yixiao Li

2024-09-06

Single group, single predictor1

Single group, multiple predictors

Multigroup, single predictor

Single group, single predictor¹