A simulated construct-validation dataset for confirmatory measurement, measurement-invariance, and theory-specified nomological-network examples. Three latent constructs are measured by multiple indicators, an observed outcome is available, and responses were collected in two administration groups.
Format
A data frame with 800 rows and 13 columns:
- ag1, ag2, ag3, ag4
Agency indicators. Population standardized loadings .80, .75, .70, .78.
- pe1, pe2, pe3, pe4
Persistence indicators. Population standardized loadings .78, .72, .76, .70.
- sd1, sd2, sd3
Social desirability indicators. Population standardized loadings .70, .75, .65.
- Performance
Observed outcome score (population mean 70, SD 10).
- group
Administration group: a factor with levels
"online"and"paper"(400 cases each).
Details
Within each group, the population structural model is:
Persistence is regressed on Agency with a standardized coefficient of .45;
Performance is regressed on Agency (.40) and not on Persistence (0);
Agency and Social desirability are uncorrelated (0).
Because Persistence is correlated with Agency, Persistence and Performance are still correlated marginally (about .18 in the population) even though the direct Persistence-to-Performance path is zero. This makes the dataset useful for teaching the difference between a marginal association and a theory-specified structural path.
Measurement-invariance teaching features: all loadings are equal across
groups, the latent Agency mean is .25 SD higher in the paper group, and the
intercept of ag3 is .50 higher in the paper group. The ag3 intercept is
therefore a known source of scalar non-invariance. Indicators are reported
on a continuous rating metric (population mean 4, SD 1 in the online
group) and rounded to two decimals.
Examples
str(nomo_demo_network)
#> 'data.frame': 800 obs. of 13 variables:
#> $ ag1 : num 5.87 5.89 2.79 6.42 5.25 4.91 4.45 4.15 5.25 5.09 ...
#> $ ag2 : num 4.43 5.96 3.14 5.5 3.85 4.94 5.25 3.13 5.02 4.32 ...
#> $ ag3 : num 5.38 4.58 1.65 5.26 3.5 4.99 3.17 4.72 4.65 5.42 ...
#> $ ag4 : num 4.25 5 2.48 5.35 3.66 6.04 3.92 4.14 5.45 4.49 ...
#> $ pe1 : num 4.61 3.84 3.41 4.96 2.92 5.46 4.88 3.82 4.3 4.47 ...
#> $ pe2 : num 6.26 4.79 3.34 3.24 4.13 4.95 4.95 4.81 3.88 4.15 ...
#> $ pe3 : num 4.81 5.1 2.96 5.11 3.96 4.8 5.19 4.94 4.53 4.07 ...
#> $ pe4 : num 4.39 2.84 4.52 3.37 3.99 4.53 3.92 5.07 5.02 5.19 ...
#> $ sd1 : num 6.4 3.24 3.1 3.18 4.61 3.34 4.91 3.7 2.71 4.98 ...
#> $ sd2 : num 4.6 2.18 3.65 2.69 4.34 4.66 4.71 4.62 2.6 4.13 ...
#> $ sd3 : num 4.72 3.6 1.93 3.08 3.39 2.52 4.57 2.93 1.94 4.5 ...
#> $ Performance: num 76.1 74.7 52.8 69.2 79.2 71.1 62.7 83.1 73 64.5 ...
#> $ group : Factor w/ 2 levels "online","paper": 1 1 1 1 1 1 1 1 1 1 ...
table(nomo_demo_network$group)
#>
#> online paper
#> 400 400