Reliability‑Corrected Single‑Item SEM
relcorr_single_item.RdReplace (some of) the first‑order latent variables in a lavaan measurement model by single composite indicators whose error variances are fixed from Cronbach's \(\alpha\). The function returns a modified lavaan model syntax together with an augmented data set that contains the newly created composite variables, so that you can fit the full SEM in a single step.
Arguments
- syntax
A character string containing lavaan model syntax. Must at least include the measurement relations (
=~).- data
A
data.frame,tibbleor object coercible to a data frame that holds the raw observed indicators.- choose
Optional. Character vector with the names of the latent variables you wish to replace by single indicators. Defaults to all first‑order latent variables in
syntax.- scale.corrected
Should reliability-corrected items be scale-corrected? If
TRUEreliability-corrected single items are corrected for differences in factor loadings between the items. Default isTRUE.- warn.lav
Should warnings from
lavaan::cfabe displayed? IfFALSE, they are suppressed.
Value
An object of S3 class modsem_relcorr (a named list) with elements:
syntaxModified lavaan syntax string.
dataData frame with additional composite indicator columns.
parTableParameter table corresponding to `syntax`.
reliabilityNamed numeric vector of reliabilities (one per latent variable).
AVENamed numeric vector with Average Variance Extracted values.
lVsCharacter vector of latent variables that were corrected.
single.itemsCharacter vector with names for the generated reliability corrected items
Details
The resulting object can be fed directly into modsem or lavaan::sem
by supplying syntax = $syntax and data = $data.
Examples
# \dontrun{
tpb_uk <- "
# Outer Model (Based on Hagger et al., 2007)
ATT =~ att3 + att2 + att1 + att4
SN =~ sn4 + sn2 + sn3 + sn1
PBC =~ pbc2 + pbc1 + pbc3 + pbc4
INT =~ int2 + int1 + int3 + int4
BEH =~ beh3 + beh2 + beh1 + beh4
# Inner Model (Based on Steinmetz et al., 2011)
INT ~ ATT + SN + PBC
BEH ~ INT + PBC
BEH ~ INT:PBC
"
corrected <- relcorr_single_item(syntax = tpb_uk, data = TPB_UK)
print(corrected)
#> Average Variance Extracted:
#> ATT: 0.773
#> SN: 0.759
#> PBC: 0.765
#> INT: 0.790
#> BEH: 0.769
#>
#> Chronbach's Alpha:
#> ATT: 0.941
#> SN: 0.917
#> PBC: 0.931
#> INT: 0.984
#> BEH: 0.942
#>
#> Generated Syntax:
#> INT ~ ATT
#> INT ~ SN
#> INT ~ PBC
#> BEH ~ INT
#> BEH ~ PBC
#> BEH ~ INT:PBC
#> ATT =~ 1*composite_ATT_
#> SN =~ 1*composite_SN_
#> PBC =~ 1*composite_PBC_
#> INT =~ 1*composite_INT_
#> BEH =~ 1*composite_BEH_
#> composite_ATT_ ~~ 0.261238305705924*composite_ATT_
#> composite_SN_ ~~ 0.168932578899161*composite_SN_
#> composite_PBC_ ~~ 0.339024670490075*composite_PBC_
#> composite_INT_ ~~ 0.0800211390420975*composite_INT_
#> composite_BEH_ ~~ 0.36503257276914*composite_BEH_
#>
#> Generated Items:
#> 'data.frame': 1169 obs. of 5 variables:
#> $ composite_ATT_: num 6.03 5.49 2.19 6.03 4.94 ...
#> $ composite_SN_ : num 5.57 4.07 3 5.57 4.5 ...
#> $ composite_PBC_: num 4.44 5 1.94 6.39 6.11 ...
#> $ composite_INT_: num 4.06 4.56 1.01 5.32 5.32 ...
#> $ composite_BEH_: num 1.11 4.17 1.39 3.06 5.84 ...
syntax <- corrected$syntax
data <- corrected$data
est_dca <- modsem(syntax, data = data, method = "dblcent")
est_lms <- modsem(syntax, data = data, method="lms", nodes=32)
summary(est_lms)
#>
#> modsem (version 1.0.12):
#>
#> Estimator LMS
#> Optimization method EMA-NLMINB
#> Number of observations 1169
#> Number of iterations 103
#> Loglikelihood -9397.25
#> Akaike (AIC) 18832.5
#> Bayesian (BIC) 18928.72
#>
#> Numerical Integration:
#> Points of integration (per dim) 32
#> Dimensions 1
#> Total points of integration 32
#>
#> Fit Measures for Baseline Model (H0):
#> Loglikelihood -9543.07
#> Akaike (AIC) 19122.14
#> Bayesian (BIC) 19213.29
#> Chi-square 34.39
#> Degrees of Freedom (Chi-square) 2
#> P-value (Chi-square) 0.000
#> RMSEA 0.118
#>
#> Comparative Fit to H0 (LRT test):
#> Loglikelihood change 145.82
#> Difference test (D) 291.63
#> Degrees of freedom (D) 1
#> P-value (D) 0.000
#>
#> R-Squared Interaction Model (H1):
#> INT 0.857
#> BEH 0.937
#> R-Squared Baseline Model (H0):
#> INT 0.858
#> BEH 0.873
#> R-Squared Change (H1 - H0):
#> INT -0.001
#> BEH 0.064
#>
#> Parameter Estimates:
#> Coefficients unstandardized
#> Information observed
#> Standard errors standard
#>
#> Latent Variables:
#> Estimate Std.Error z.value P(>|z|)
#> ATT =~
#> cmpst_ATT_ 1.000
#> SN =~
#> compst_SN_ 1.000
#> PBC =~
#> cmpst_PBC_ 1.000
#> INT =~
#> cmpst_INT_ 1.000
#> BEH =~
#> cmpst_BEH_ 1.000
#>
#> Regressions:
#> Estimate Std.Error z.value P(>|z|)
#> INT ~
#> ATT -0.022 0.042 -0.528 0.597
#> SN 0.015 0.037 0.390 0.697
#> PBC 0.991 0.046 21.712 0.000
#> BEH ~
#> PBC 0.726 0.045 16.005 0.000
#> INT 0.307 0.042 7.262 0.000
#> INT:PBC 0.148 0.008 18.024 0.000
#>
#> Intercepts:
#> Estimate Std.Error z.value P(>|z|)
#> .cmpst_PBC_ 4.323 0.064 67.722 0.000
#> .cmpst_ATT_ 4.246 0.063 66.982 0.000
#> .compst_SN_ 3.797 0.041 93.173 0.000
#> .cmpst_INT_ 3.835 0.066 58.497 0.000
#> .cmpst_BEH_ 2.891 0.077 37.603 0.000
#>
#> Covariances:
#> Estimate Std.Error z.value P(>|z|)
#> ATT ~~
#> SN 1.907 0.104 18.262 0.000
#> PBC ~~
#> ATT 3.964 0.180 21.998 0.000
#> SN 2.028 0.107 19.004 0.000
#>
#> Variances:
#> Estimate Std.Error z.value P(>|z|)
#> .cmpst_PBC_ 0.339
#> .cmpst_ATT_ 0.261
#> .compst_SN_ 0.169
#> .cmpst_INT_ 0.080
#> .cmpst_BEH_ 0.365
#> ATT 4.438 0.194 22.837 0.000
#> SN 1.773 0.080 22.071 0.000
#> PBC 4.427 0.197 22.473 0.000
#> .INT 0.709 0.046 15.353 0.000
#> .BEH 0.376 0.039 9.694 0.000
#>
# }