A toy dataset containing measures on 6 items (y1-y6), 3 within-level covariates (x1-x3) and 2 between-level covariates (w1-w2). The data is clustered (200 clusters of size 5, 10, 15 and 20), and the cluster variable is “cluster”.

data(Demo.twolevel)

Format

A data frame of 2500 observations of 12 variables. clusters.

y1

item 1

y2

item 2

y3

item 3

y4

item 4

y5

item 5

y6

item 6

x1

within-level covariate 1

x2

within-level covariate 2

x3

within-level covariate 3

w1

between-level covariate 1

w2

between-level covariate 2

cluster

cluster variable

Examples

head(Demo.twolevel)
#>           y1         y2         y3         y4         y5         y6         x1
#> 1  0.2293216  1.3555232 -0.6911702  0.8028079 -0.3011085 -1.7260671  1.1739003
#> 2  0.3085801 -1.8624397 -2.4179783  0.7659289  1.6750617  1.1764210 -1.0039958
#> 3  0.2004934 -1.3400514  0.4376087  1.1974194  1.1951594  1.4988962 -0.4402545
#> 4  1.0447982 -0.9624490 -0.4464898 -0.2027252 -0.4590574  1.1734061 -0.6253657
#> 5  0.6881792 -0.4565633 -0.6422296  0.9900408  1.7662535  0.7944601 -0.8450025
#> 6 -2.0687644 -0.5997856  0.3148418  0.6764432 -0.6519928  1.8405605 -0.7831784
#>            x2         x3         w1         w2 cluster
#> 1 -0.62315173  0.6470414 -0.2479975 -0.4989800       1
#> 2 -0.56689380  0.0201264 -0.2479975 -0.4989800       1
#> 3 -2.13432572 -0.4591246 -0.2479975 -0.4989800       1
#> 4 -0.33688869  1.2852093 -0.2479975 -0.4989800       1
#> 5 -0.04229954  1.5598970 -0.2479975 -0.4989800       1
#> 6 -0.22441996 -0.3814231 -2.3219338 -0.6910567       2

model <- '
    level: 1
        fw =~ y1 + y2 + y3
        fw ~ x1 + x2 + x3
    level: 2
        fb =~ y1 + y2 + y3
        fb ~ w1 + w2
'
fit <- sem(model, data = Demo.twolevel, cluster = "cluster")
summary(fit)
#> lavaan 0.6-20 ended normally after 36 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        20
#> 
#>   Number of observations                          2500
#>   Number of clusters [cluster]                     200
#> 
#> Model Test User Model:
#>                                                       
#>   Test statistic                                 8.092
#>   Degrees of freedom                                10
#>   P-value (Chi-square)                           0.620
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> 
#> Level 1 [within]:
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   fw =~                                               
#>     y1                1.000                           
#>     y2                0.774    0.032   24.349    0.000
#>     y3                0.734    0.030   24.052    0.000
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   fw ~                                                
#>     x1                0.510    0.023   22.387    0.000
#>     x2                0.407    0.022   18.489    0.000
#>     x3                0.205    0.021    9.776    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .y1                0.986    0.043   22.802    0.000
#>    .y2                1.066    0.039   27.616    0.000
#>    .y3                1.011    0.035   29.287    0.000
#>    .fw                0.546    0.032   16.848    0.000
#> 
#> 
#> Level 2 [cluster]:
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   fb =~                                               
#>     y1                1.000                           
#>     y2                0.717    0.047   15.182    0.000
#>     y3                0.587    0.043   13.503    0.000
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   fb ~                                                
#>     w1                0.165    0.078    2.099    0.036
#>     w2                0.131    0.076    1.721    0.085
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .y1                0.024    0.075    0.327    0.744
#>    .y2               -0.016    0.060   -0.267    0.789
#>    .y3               -0.042    0.054   -0.775    0.439
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .y1                0.058    0.043    1.346    0.178
#>    .y2                0.120    0.031    3.922    0.000
#>    .y3                0.149    0.028    5.376    0.000
#>    .fb                0.899    0.110    8.194    0.000
#>