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| # title Bivariate Latent Change Score Model | |
| # GitHub https://github.com/ulrich-schroeders/syntax-publications | |
| # date 2016-11-06 | |
| # version 1.0.0 | |
| # reference Schroeders, U., Schipolowski, S., Zettler, I., Golle, J., & Wilhelm, O. (2016). Do the smart get smarter? Development of fluid and crystallized intelligence in 3rd grade. Intelligence. https://doi.org/10.1016/j.intell.2016.08.003 | |
| library(lavaan) | |
| mod.lc <- ' | |
| # ----------- | |
| # gf | |
| # ----------- | |
| # measurement part, equal factor loadings across time | |
| gf_pre =~ gfv1 + lam2*gfn1 + lam3*gff1 | |
| gf_post =~ gfv2 + lam2*gfn2 + lam3*gff2 | |
| gf_change =~ 0 # introduction of the latent difference variable | |
| # (co)variances | |
| gf_post ~~ 0*gf_post # no residual, perfect regression | |
| gf_pre ~~ NA*gf_pre # freely estimate gf_pre variance | |
| gf_change ~~ NA*gf_change # freely estimate change gf variance | |
| # prediction part, difference factor | |
| gf_post ~ 1*gf_pre # perfect regression of gf_pre on gf_post | |
| gf_post ~ 1*gf_change # perfect regression of gf_change on gf_post | |
| gf_change ~~ gf_pre # gf_pre covaries with gf_change | |
| # mean structure | |
| gf_pre ~ 0*1 # fixing the mean to zero | |
| gf_post ~ 0*1 # fixing the mean to zero | |
| gf_change ~ NA*1 # estimating the mean for the gf_change factor freely | |
| # equal intercepts across time | |
| gfv1 ~ int1*1 | |
| gfv2 ~ int1*1 | |
| gfn1 ~ int2*1 | |
| gfn2 ~ int2*1 | |
| gff1 ~ int3*1 | |
| gff2 ~ int3*1 | |
| # residual variances across time | |
| gfv1 ~~ res1*gfv1 | |
| gfn1 ~~ res2*gfn1 | |
| gff1 ~~ res3*gff1 | |
| gfv2 ~~ res1*gfv2 | |
| gfn2 ~~ res2*gfn2 | |
| gff2 ~~ res3*gff2 | |
| # residual covariances | |
| gfv1 ~~ gfv2 | |
| gfn1 ~~ gfn2 | |
| gff1 ~~ gff2 | |
| # ----------- | |
| # gc | |
| # ----------- | |
| # measurement part, equal factor loadings across time | |
| gc_pre =~ gc1Sci + lam5*gc1Hum + lam6*gc1Soc | |
| gc_post =~ gc2Sci + lam5*gc2Hum + lam6*gc2Soc | |
| gc_change =~ 0 # introduction of the latent difference variable | |
| # (co)variances | |
| gc_post ~~ 0*gc_post # no residual, perfect regression | |
| gc_pre ~~ NA*gc_pre # freely estimate gc_pre variance | |
| gc_change ~~ NA*gc_change # freely estimate change gc variance | |
| # prediction part, difference factor | |
| gc_post ~ 1*gc_pre # perfect regression of gc_pre on gc_post | |
| gc_post ~ 1*gc_change # perfect regression of gc_change on gc_post | |
| gc_change ~~ gc_pre # gc_pre covaries with gc_change | |
| # mean structure | |
| gc_pre ~ 0*1 # fixing the mean to zero | |
| gc_post ~ 0*1 # fixing the mean to zero | |
| gc_change ~ NA*1 # estimating the mean for the gc_change factor freely | |
| # equal intercepts across time | |
| gc1Sci ~ int5*1 | |
| gc2Sci ~ int5*1 | |
| gc1Hum ~ int6*1 | |
| gc2Hum ~ int6*1 | |
| gc1Soc ~ int7*1 | |
| gc2Soc ~ int7*1 | |
| # residual variances across time | |
| gc1Sci ~~ res5*gc1Sci | |
| gc1Hum ~~ res6*gc1Hum | |
| gc1Soc ~~ res7*gc1Soc | |
| gc2Sci ~~ res5*gc2Sci | |
| gc2Hum ~~ res6*gc2Hum | |
| gc2Soc ~~ res7*gc2Soc | |
| # residual covariances | |
| gc1Sci ~~ gc2Sci | |
| gc1Hum ~~ gc2Hum | |
| gc1Soc ~~ gc2Soc | |
| # ------ | |
| # gf gc paths | |
| # ------ | |
| gf_change ~~ gc_pre | |
| gc_change ~~ gf_pre | |
| gc_pre ~~ gf_pre | |
| gc_change ~~ gf_change | |
| gf_post ~~ 0*gc_post | |
| ' | |
| fit.lc <- cfa(model=mod.lc, # model specification | |
| data=dat, # data | |
| estimator= "ML", # estimator | |
| missing="ML", # FIML | |
| orthogonal=TRUE) # all latent variables are uncorrelated | |
| summary(fit.lc, fit.measures=TRUE, standardized=TRUE) |