The goal of pinsearch is to automate the process of performing specification search in identifying noninvariant items to arrive at a partial factorial invariance model.
Installation
You can install the development version of pinsearch from GitHub with:
# install.packages("remotes")
remotes::install_github("marklhc/pinsearch")Example
This is a basic example which shows you how to solve a common problem:
library(pinsearch)
library(lavaan)
#> This is lavaan 0.6-17
#> lavaan is FREE software! Please report any bugs.
HS.model <- ' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 '
# Output the final partial invariance model, and the noninvariant items
pinSearch(HS.model, data = HolzingerSwineford1939,
group = "school", type = "intercepts")
#> $`Partial Invariance Fit`
#> lavaan 0.6.17 ended normally after 69 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 66
#> Number of equality constraints 16
#>
#> Number of observations per group:
#> Pasteur 156
#> Grant-White 145
#>
#> Model Test User Model:
#>
#> Test statistic 129.422
#> Degrees of freedom 58
#> P-value (Chi-square) 0.000
#> Test statistic for each group:
#> Pasteur 71.170
#> Grant-White 58.253
#>
#> $`Non-Invariant Items`
#> group lhs rhs type
#> 1 1 x3 intercepts
#> 2 1 x7 intercepts
# Compute dmacs effect size (added in version 0.1.2)
pinSearch(HS.model, data = HolzingerSwineford1939,
group = "school", type = "intercepts",
effect_size = TRUE,
progress = TRUE)
#>
#> [1/2] Searching for loadings noninvariance
#>
#> [2/2] Searching for intercepts noninvariance
#> | | | 0% | |================== | 25% | |==================================================== | 75%
#> $`Partial Invariance Fit`
#> lavaan 0.6.17 ended normally after 69 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 66
#> Number of equality constraints 16
#>
#> Number of observations per group:
#> Pasteur 156
#> Grant-White 145
#>
#> Model Test User Model:
#>
#> Test statistic 129.422
#> Degrees of freedom 58
#> P-value (Chi-square) 0.000
#> Test statistic for each group:
#> Pasteur 71.170
#> Grant-White 58.253
#>
#> $`Non-Invariant Items`
#> group lhs rhs type
#> 1 1 x3 intercepts
#> 2 1 x7 intercepts
#>
#> $effect_size
#> x3-visual x7-visual x3-textual x7-textual x3-speed x7-speed
#> dmacs 0.4824515 0.4161323 0.4824515 0.4161323 0.4824515 0.4161323Example 2
A simulated example with ordinal data
# Simulate data
set.seed(2110)
library(MASS)
num_obs <- 500
lambda1 <- seq(.9, .6, length.out = 7)
lambda2 <- c(lambda1[1], 1, lambda1[3:7])
cov1 <- tcrossprod(lambda1) + diag(.5, 7)
dimnames(cov1) <- list(paste0("yy", 1:7), paste0("yy", 1:7))
thres1 <- rbind(seq(-1.5, 1.5, length.out = 7))
thres2 <- rbind(c(thres1[1], 0.25, thres1[3:6], 0.3))
mean1 <- rep(0, 7)
ystar1 <- mvrnorm(num_obs, mu = mean1, Sigma = cov1)
y1 <- ystar1
cov2 <- tcrossprod(lambda1) * 1.3 + diag(.5, 7)
dimnames(cov2) <- dimnames(cov1)
mean2 <- lambda1 * .4
ystar2 <- mvrnorm(num_obs, mu = mean2, Sigma = cov2)
y2 <- ystar2
# Ordinal indicators
thres1 <- rbind(seq(-1.5, 0, length.out = 7),
seq(-0.5, 0.25, length.out = 7),
rep(1, 7))
thres2 <- rbind(c(thres1[1, 1], -0.5, thres1[1, 3:6], -0.5),
thres1[2,],
c(rep(1, 3), rep(0.5, 2), rep(1, 2)))
for (j in seq_len(ncol(ystar1))) {
y1[, j] <- findInterval(ystar1[, j], thres1[, j])
}
for (j in seq_len(ncol(ystar2))) {
y2[, j] <- findInterval(ystar2[, j], thres2[, j])
}
df <- rbind(cbind(y1, group = 1), cbind(y2, group = 2))
pinSearch(' f =~ yy1 + yy2 + yy3 + yy4 + yy5 + yy6 + yy7 ',
data = df, group = "group", type = "thresholds",
ordered = paste0("yy", 1:7),
effect_size = TRUE)
#> $`Partial Invariance Fit`
#> lavaan 0.6.17 ended normally after 52 iterations
#>
#> Estimator DWLS
#> Optimization method NLMINB
#> Number of model parameters 58
#> Number of equality constraints 24
#>
#> Number of observations per group:
#> 1 500
#> 2 500
#>
#> Model Test User Model:
#> Standard Scaled
#> Test Statistic 31.911 49.933
#> Degrees of freedom 50 50
#> P-value (Chi-square) 0.978 0.476
#> Scaling correction factor 0.745
#> Shift parameter 7.073
#> simple second-order correction
#> Test statistic for each group:
#> 1 14.835 23.461
#> 2 17.077 26.472
#>
#> $`Non-Invariant Items`
#> group lhs rhs type
#> 1 1 yy2 t1 thresholds
#> 2 2 yy7 t1 thresholds
#> 3 1 yy5 t3 thresholds
#> 4 1 yy4 t3 thresholds
#>
#> $effect_size
#> yy2-f yy4-f yy5-f yy7-f
#> dmacs 0.2376422 0.1181811 0.1662268 0.2071426