ockhamSEM is an R package for studying the fit propensity of single-group structural equation models with continuous items. Underlying support is through the lavaan package. A variety built-in graphical and text summaries are provided.
The package is introduced in Falk and Muthukrishna (2020) Parsimony in Model Selection: Tools for Assessing Fit Propensity.
# From GitHub:
# install.packages("devtools")
devtools::install_github("falkcarl/ockhamSEM")Let’s compare fit propensity for the following two models consisting of 3 variables:
p<-3 # number of variables
temp_mat <- diag(p) # identity matrix
colnames(temp_mat) <- rownames(temp_mat) <- paste0("V", seq(1, p))mod1a <- 'V3 ~ V1 + V2
V1 ~~ 0*V2'
mod2a <- 'V3 ~ V1
V2 ~ V3'
mod1a.fit <- sem(mod1a, sample.cov=temp_mat, sample.nobs=500)
mod2a.fit <- sem(mod2a, sample.cov=temp_mat, sample.nobs=500)Here we use the onion method to generate random correlation matrices and will compare fit propensity for the SRMR and CFI fit measures.
res <- run.fitprop(mod1a.fit, mod2a.fit, fit.measure=c("srmr","cfi"),
rmethod="onion",reps=1000)Output:
[1] "Generate matrices"
[1] "Fitting models"
Summarize:
summary(res)Output:
Quantiles for each model and fit measure:
Model 1
srmr cfi
0% 0.001 0.000
10% 0.041 0.227
20% 0.091 0.413
30% 0.133 0.574
40% 0.177 0.682
50% 0.219 0.778
60% 0.269 0.852
70% 0.316 0.922
80% 0.406 0.969
90% 0.635 0.994
100% 11.059 1.000
Model 2
srmr cfi
0% 0.000 0.000
10% 0.031 0.129
20% 0.051 0.257
30% 0.079 0.394
40% 0.104 0.522
50% 0.133 0.656
60% 0.162 0.763
70% 0.202 0.870
80% 0.239 0.936
90% 0.294 0.982
100% 0.400 1.000
Information about replications for each model and fit measure:
Model 1
Mean across replications
srmr cfi
0.366 0.693
Median across replications
srmr cfi
0.219 0.778
Number of finite values
srmr cfi
999 999
Number of NA values
srmr cfi
1 1
Model 2
Mean across replications
srmr cfi
0.148 0.601
Median across replications
srmr cfi
0.133 0.656
Number of finite values
srmr cfi
1000 1000
Number of NA values
srmr cfi
0 0
Effect Sizes for Differences in Model Fit:
srmr
Model 1 vs. Model 2
Cohen's d: -2.386
Cliff's delta: 0.342
Komolgorov Smirnov: 0.273
cfi
p-value will be approximate in the presence of ties
Model 1 vs. Model 2
Cohen's d: -2.057
Cliff's delta: 0.168
Komolgorov Smirnov: 0.145
Plot:
plot(res)Output:
