For those interested... I made R implement LCS, it's actually pretty flexible... enjoy!
#as with Mplus code, I suggest you rename your T1 and T2 variables obsY1 and obsY2 first
install.packages("lavaan") #you need to install lavaan first
library(lavaan) #you need to call in lavaan first
#in lavaan the model and data are 2 entities, I like this, they become connected after defining the model
#first the model
LCS2waves <- ' LatY1 =~ 1*obsY1 #define latents behind the observed
obsY1~~ measerr*obsY1 # same measurement error measerr across time
obsY1~0*1 #intercept of 1-indicator@0 to identify the mean of the latent; if free obsY1~1
LatY2 =~ 1*obsY2; #define latents behind the observed
obsY2~~ measerr*obsY2 #same measurement error measerr across time
obsY2~0*1 #intercept of 1-indicator@0 to identify the mean of the latent; if free obsY1~1
#LCS part
LCS21 =~ 1*obsY2 #define LCS on the second variable in subtraction
LatY2 =~ 1*LatY1; # autoregression AR1 @1
LatY2~~0*LatY2 #all LatY2 variance is explained, no error left
LatY1~1 # LatY1 mean of first estimated
LatY2~0*1 # LatY2 intercept =0 so LCS21 mean can be identified
#LCS21~~0*LCS21 #no need to set it to 0 per se, but this commonly becomes <0
LCS21~1 # LCS21 mean or intercept estimated
#this is the mean of change, IF nothing points to it, if anything points to it, need to center them to interpret this intercept
LCS21~LatY1 #proportional growth, this is not needed, if you take it out you will have a covariance between them estimated
'
#now one can fit the model above to some (any) data
fit <- sem(model = LCS2waves, data = YOURDATA)
# show results
summary(fit, fit.measures=TRUE)
#mine showed something like:
lavaan (0.5-23.1097) converged normally after 46 iterations
Number of observations 61
Estimator ML
Minimum Function Test Statistic NA
Degrees of freedom -1
Minimum Function Value 0.0000000000000
User model versus baseline model:
Comparative Fit Index (CFI) NA
Tucker-Lewis Index (TLI) NA
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -409.528
Loglikelihood unrestricted model (H1) -409.528
Number of free parameters 6
Akaike (AIC) 831.056
Bayesian (BIC) 843.721
Sample-size adjusted Bayesian (BIC) 824.846
Root Mean Square Error of Approximation:
RMSEA NA
90 Percent Confidence Interval NA NA
P-value RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Information Expected
Standard Errors Standard
Latent Variables:
Estimate Std.Err z-value P(>|z|)
LatY1 =~
obsY1 1.000
LatY2 =~
obsY2 1.000
LCS21 =~
obsY2 1.000
LatY2 =~
LatY1 1.000
Regressions:
Estimate Std.Err z-value P(>|z|)
LCS21 ~
LatY1 0.568 0.423 1.341 0.180
Intercepts:
Estimate Std.Err z-value P(>|z|)
.obsY1 0.000
.obsY2 0.000
LatY1 9.131 0.912 10.009 0.000
LatY2 0.000
.LCS21 3.569 3.742 0.954 0.340
Variances:
Estimate Std.Err z-value P(>|z|)
.obsY1 (msrr) 51.146 14.017 3.649 0.000
.obsY2 (msrr) 51.146 14.017 3.649 0.000
LatY2 0.000
LatY1 -0.376 10.659 -0.035 0.972
.LCS21 -5.233 14.091 -0.371 0.710
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This paper introduces LCS amazingly simply and intuitively, a graphical depiction below; when it's going to be published maybe the R code will accompany it.
Berggren, R., Nilsson, J., Brehmer, Y., Schmiedek, F., & Lövdén, M. (2018). No evidence that foreign language learning in older age improve cognitive ability A RCT.
