reliability-corrected single items
relcorr_items.RmdReliablity-Corrected Single Items
If wanted, indicators for latent variables can be replaced with
reliablity corrected single items, using Chronbach’s
.
This can either be done using the relcorr_single_item
function, returning the altered model syntax and data, or via the
rcs argument in modsem. Here we can see an
example using the relcorr_single_item function:
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)
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_ ~~ 0.230703252252833*composite_ATT_
#> composite_SN_ ~~ 0.219569422798239*composite_SN_
#> composite_PBC_ ~~ 0.269459429965901*composite_PBC_
#> composite_INT_ ~~ 0.0783705643995773*composite_INT_
#> composite_BEH_ ~~ 0.276556964349188*composite_BEH_
#>
#> Generated Items:
#> 'data.frame': 1169 obs. of 5 variables:
#> $ composite_ATT_: num 5.5 5 2 5.5 4.5 1 1 1 4.25 6.25 ...
#> $ composite_SN_ : num 6.5 4.75 3.5 6.5 5.25 3 2.25 4 4.5 6 ...
#> $ composite_PBC_: num 4 4.5 1.75 5.75 5.5 1 1 1 5 5.75 ...
#> $ composite_INT_: num 4 4.5 1 5.25 5.25 1 1 1 5 5 ...
#> $ composite_BEH_: num 1 3.75 1.25 2.75 5.25 1 1 1 2.5 5.5 ...Here we can see that relcorr_single_item returns a new
model syntax, and a new data.frame containing the generated
items. Additionally, it also returns the Chronbach’s
and average variance extraced (AVE) for the different
constructs in the model. The syntax and data can be extracted using the
$ operator, and used to estimate the model.
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 1.0.11):
#>
#> Estimator LMS
#> Optimization method EMA-NLMINB
#> Number of observations 1169
#> Number of iterations 49
#> Loglikelihood -7276.79
#> Akaike (AIC) 14591.57
#> Bayesian (BIC) 14687.79
#>
#> Numerical Integration:
#> Points of integration (per dim) 32
#> Dimensions 1
#> Total points of integration 32
#>
#> Fit Measures for Baseline Model (H0):
#> Loglikelihood -9352.47
#> Akaike (AIC) 18740.95
#> Bayesian (BIC) 18832.1
#> Chi-square 34.76
#> Degrees of Freedom (Chi-square) 2
#> P-value (Chi-square) 0.000
#> RMSEA 0.118
#>
#> Comparative Fit to H0 (LRT test):
#> Loglikelihood change 2075.69
#> Difference test (D) 4151.38
#> Degrees of freedom (D) 1
#> P-value (D) 0.000
#>
#> R-Squared Interaction Model (H1):
#> INT 0.865
#> BEH 0.940
#> R-Squared Baseline Model (H0):
#> INT 0.856
#> BEH 0.869
#> R-Squared Change (H1 - H0):
#> INT 0.009
#> BEH 0.071
#>
#> Parameter Estimates:
#> Coefficients unstandardized
#> Information observed
#> Standard errors standard
#>
#> Latent Variables:
#> Estimate Std.Error z.value P(>|z|)
#> PBC =~
#> cmpst_PBC_ 1.000
#> ATT =~
#> cmpst_ATT_ 1.000
#> SN =~
#> compst_SN_ 1.000
#> INT =~
#> cmpst_INT_ 1.000
#> BEH =~
#> cmpst_BEH_ 1.000
#>
#> Regressions:
#> Estimate Std.Error z.value P(>|z|)
#> INT ~
#> PBC 1.054 0.053 19.825 0.000
#> ATT 0.000 0.051 -0.008 0.993
#> SN 0.026 0.030 0.871 0.384
#> BEH ~
#> PBC 0.719 0.043 16.802 0.000
#> INT 0.301 0.036 8.372 0.000
#> PBC:INT 0.150 0.008 18.283 0.000
#>
#> Intercepts:
#> Estimate Std.Error z.value P(>|z|)
#> .cmpst_PBC_ 3.956 0.031 128.919 0.000
#> .cmpst_ATT_ 3.926 0.038 104.339 0.000
#> .compst_SN_ 4.466 0.038 117.695 0.000
#> .cmpst_INT_ 3.851 0.038 100.233 0.000
#> .cmpst_BEH_ 2.660 0.051 52.364 0.000
#>
#> Covariances:
#> Estimate Std.Error z.value P(>|z|)
#> PBC ~~
#> ATT 3.516 0.091 38.798 0.000
#> SN 2.296 0.086 26.562 0.000
#> ATT ~~
#> SN 2.187 0.091 24.055 0.000
#>
#> Variances:
#> Estimate Std.Error z.value P(>|z|)
#> .cmpst_PBC_ 0.269
#> .cmpst_ATT_ 0.231
#> .compst_SN_ 0.220
#> .cmpst_INT_ 0.078
#> .cmpst_BEH_ 0.277
#> PBC 3.905 0.094 41.382 0.000
#> ATT 3.916 0.127 30.785 0.000
#> SN 2.527 0.104 24.215 0.000
#> .INT 0.695 0.044 15.773 0.000
#> .BEH 0.328 0.032 10.347 0.000Alternatively, it is possible to use the rcs argument in
the modsem function to call
relcorr_single_item before estimating the model.
est_dca <- modsem(tpb_uk, data = TPB_UK, method = "dblcent", rcs = TRUE)
est_lms <- modsem(tpb_uk, data = TPB_UK, method = "lms", rcs = TRUE)
#> Warning: It is recommended that you have at least 32 nodes for interaction
#> effects between exogenous and endogenous variables in the lms approach 'nodes =
#> 24'Choosing Variables
If you don’t want to use reliablity-corrected single items for all of
the latent variables in the model, you can use the choose
argument in relcorr_single_item (orrcs.choose
in modsem) to select which set of indicators to
replace.
relcorr_single_item(syntax = tpb_uk, data = TPB_UK,
choose = c("ATT", "SN", "PBC", "INT"))
#> Average Variance Extracted:
#> ATT: 0.773
#> SN: 0.759
#> PBC: 0.764
#> INT: 0.790
#>
#> Chronbach's Alpha:
#> ATT: 0.941
#> SN: 0.917
#> PBC: 0.931
#> INT: 0.984
#>
#> Generated Syntax:
#> INT ~ ATT
#> INT ~ SN
#> INT ~ PBC
#> BEH ~ INT
#> BEH ~ PBC
#> BEH ~ INT:PBC
#> BEH =~ beh3
#> BEH =~ beh2
#> BEH =~ beh1
#> BEH =~ beh4
#> ATT =~ 1*composite_ATT_
#> SN =~ 1*composite_SN_
#> PBC =~ 1*composite_PBC_
#> INT =~ 1*composite_INT_
#> composite_ATT_ ~~ 0.230703252252833*composite_ATT_
#> composite_SN_ ~~ 0.219569422798239*composite_SN_
#> composite_PBC_ ~~ 0.269459429965901*composite_PBC_
#> composite_INT_ ~~ 0.0783705643995773*composite_INT_
#>
#> Generated Items:
#> 'data.frame': 1169 obs. of 4 variables:
#> $ composite_ATT_: num 5.5 5 2 5.5 4.5 1 1 1 4.25 6.25 ...
#> $ composite_SN_ : num 6.5 4.75 3.5 6.5 5.25 3 2.25 4 4.5 6 ...
#> $ composite_PBC_: num 4 4.5 1.75 5.75 5.5 1 1 1 5 5.75 ...
#> $ composite_INT_: num 4 4.5 1 5.25 5.25 1 1 1 5 5 ...
est_dca <- modsem(tpb_uk, data = TPB_UK, method = "dblcent", rcs = TRUE,
rcs.choose = c("ATT", "SN", "PBC", "INT"))
summary(est_dca)
#> Estimating baseline model (H0)
#> modsem (version 1.0.11, approach = dblcent):
#>
#> Interaction Model Fit Measures (H1):
#> Loglikelihood -18110.30
#> Akaike (AIC) 36270.60
#> Bayesian (BIC) 36397.20
#> Chi-square 1328.25
#> Degrees of Freedom 20
#> P-value (Chi-square) 0.000
#> RMSEA 0.237
#> CFI 0.891
#> SRMR 0.051
#>
#> Fit Measures for Baseline Model (H0):
#> Loglikelihood -18232.48
#> Akaike (AIC) 36512.97
#> Bayesian (BIC) 36634.50
#> Chi-square 1572.62
#> Degrees of Freedom 21
#> P-value (Chi-square) 0.000
#> RMSEA 0.251
#> CFI 0.871
#> SRMR 0.075
#>
#> Comparative Fit to H0 (LRT test):
#> Chi-square diff 244.368
#> Degrees of freedom diff 1
#> P-value (LRT) 0.000
#>
#> R-Squared Interaction Model (H1):
#> INT 0.858
#> BEH 0.908
#> R-Squared Baseline Model (H0):
#> INT 0.859
#> BEH 0.874
#> R-Squared Change (H1 - H0):
#> INT -0.001
#> BEH 0.034
#>
#> lavaan 0.6-19 ended normally after 61 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 25
#>
#> Number of observations 1169
#>
#> Model Test User Model:
#>
#> Test statistic 1328.248
#> Degrees of freedom 20
#> P-value (Chi-square) 0.000
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> BEH =~
#> beh3 1.000
#> beh2 0.986 0.013 74.469 0.000
#> beh1 0.822 0.019 43.579 0.000
#> beh4 0.811 0.019 42.331 0.000
#> ATT =~
#> composite_ATT_ 1.000
#> SN =~
#> composite_SN_ 1.000
#> PBC =~
#> composite_PBC_ 1.000
#> INT =~
#> composite_INT_ 1.000
#> INTPBC =~
#> cmps_INT__PBC_ 1.000
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> INT ~
#> ATT 0.002 0.045 0.034 0.973
#> SN -0.009 0.032 -0.288 0.773
#> PBC 1.075 0.050 21.585 0.000
#> BEH ~
#> INT 0.649 0.038 17.092 0.000
#> PBC 0.386 0.044 8.709 0.000
#> INTPBC 0.125 0.008 16.583 0.000
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> ATT ~~
#> SN 2.028 0.111 18.255 0.000
#> PBC 3.242 0.148 21.897 0.000
#> INTPBC 0.250 0.199 1.254 0.210
#> SN ~~
#> PBC 2.147 0.113 19.065 0.000
#> INTPBC -0.142 0.164 -0.864 0.387
#> PBC ~~
#> INTPBC 0.401 0.197 2.041 0.041
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .composite_ATT_ 0.231
#> .composite_SN_ 0.220
#> .composite_PBC_ 0.269
#> .composite_INT_ 0.078
#> .beh3 0.481 0.031 15.616 0.000
#> .beh2 0.535 0.032 16.684 0.000
#> .beh1 1.784 0.079 22.695 0.000
#> .beh4 1.863 0.082 22.795 0.000
#> .cmps_INT__PBC_ 0.000
#> .BEH 0.488 0.033 14.625 0.000
#> ATT 3.673 0.161 22.748 0.000
#> SN 2.423 0.109 22.168 0.000
#> PBC 3.604 0.160 22.496 0.000
#> .INT 0.686 0.044 15.440 0.000
#> INTPBC 11.858 0.490 24.176 0.000