Simulated two-factor item data with known teaching features

A simulated scale-development dataset with two correlated latent factors and five candidate indicators per factor. Because the population model is known, learners can compare nomologR evidence with the structure that actually generated the data.

Usage

nomo_demo_continuous

Format

A data frame with 500 rows and 10 numeric columns:

a1, a2, a3, a4, a5

Indicators written for factor A. Population standardized loadings are .80, .75, .70, .72, and .45 (with a .35 cross-loading on factor B for a5).

b1, b2, b3, b4, b5

Indicators written for factor B. Population standardized loadings are .78, .74, .80, .70, and .30.

Source

Simulated with a fixed seed by data-raw/nomo_demo.R in the package source repository.

Details

The data are deliberately imperfect in ways that scale developers routinely encounter:

• a5 cross-loads on both factors (population loadings .45 and .35);

• b5 is a weak indicator (population loading .30);

• a2 (15 cases) and b3 (12 cases) contain values missing completely at random.

These features are included so that item-audit, factor-retention, and EFA output have something substantive to explain. They are not instructions to delete a5 or b5; whether such items remain depends on theory, content coverage, and later evidence.

Population model: factors A and B are standard normal with correlation .40. Each indicator is a linear function of its factor(s) plus normal unique variance chosen so that the indicator has unit population variance. Scores are reported on a continuous rating metric (population mean 4, SD 1) and rounded to two decimals; the linear transformation does not affect correlations or standardized estimates.

See also

nomo_demo_ordinal for five-category ordered versions of the same latent responses and nomo_demo_network for a multi-construct validation study.

Examples

str(nomo_demo_continuous)
#> 'data.frame':	500 obs. of  10 variables:
#>  $ a1: num  2.23 3.47 4.8 2.87 5.22 4.02 3.23 3.12 3.62 4.66 ...
#>  $ a2: num  1.46 3.06 4.16 2.46 3.71 6.06 4.16 3.45 NA 5.27 ...
#>  $ a3: num  2.25 4.71 4.08 3.45 5.94 4.3 3.39 3.41 3.21 5.31 ...
#>  $ a4: num  2.59 3.39 4.59 3.85 4.01 3.65 4.09 3.81 4.77 5.16 ...
#>  $ a5: num  1.85 3.23 4.54 4.22 3.62 4.67 4.14 3.46 4.95 3.08 ...
#>  $ b1: num  2.67 4.05 5.31 4.6 3.57 3.11 4.16 3.99 3.49 2.71 ...
#>  $ b2: num  4.21 3.91 3.65 3.72 3.94 3.01 4.32 2.72 3.17 3.95 ...
#>  $ b3: num  2.33 4.72 4.85 4.63 2.84 2.95 3.75 4.02 3.69 3.08 ...
#>  $ b4: num  4.79 3.72 4.24 4.27 4.6 2.28 5.01 4.62 2.94 2.87 ...
#>  $ b5: num  3.42 4.47 5.4 4.38 3.87 2.97 4.75 5.63 3.65 2.97 ...
colSums(is.na(nomo_demo_continuous))
#> a1 a2 a3 a4 a5 b1 b2 b3 b4 b5 
#>  0 15  0  0  0  0  0 12  0  0 

scr <- nomo_screen(nomo_demo_continuous)
scr
#> <nomo_screen> Item and data audit
#> Cases: 500 | Candidate items: 10
#> Items with missing responses: 2 | Constant: 0 | All missing: 0
#> Relationship diagnostics: 10 eligible items | 10 item-rest estimates
#> Response concentration flags: 0 | Near-zero variance: 0
#> Decision log: 3 info, 1 review, 0 concern
#> No rows or items were removed or modified.