# Partial Least Squares structural equation modeling

Im calculating a Structural Equation model with Partial Least Squares (with R).

Lets say a simple example:

• two Response values (R1, R2) are combined to a latent variable RespLV = weight1*R1 + weight2*R2
• And a few covariates are also combined into latent variables (CoefLV1, CoefLV2, ...)
• All latent Variables are standardized to with mean=0 and variance=1
• Now a regression is performed with the result RespLV = beta1 * CoefLV1 + beta2 * CoefLV2 + ...

It is now possible to do a prediction on the standardized RespLV. Is there a possibility to to a prediction on the unstandardized RespLV?

I think (but, not too sure, though) that you can obtain non-standardized scores by using plspm's plspm.fit() function. It has the argument scaled, which is TRUE by default. If you set it to FALSE (also, scaling should be NULL), then scores component of the resulting object should contain non-standardized values (http://cran.r-project.org/web/packages/plspm/plspm.pdf, p. 24):

score Matrix of latent variables used to estimate the inner model. If scaled=FALSE then scores are latent variables calculated with the original data (non-standardized).

In the most software (e.g. SmartPLS, plspm) allowing you to estimate PLS-SEM models you can obtain the latent variable scores. This scores can then be used for certain kind of predictions using standard OLS regressions.

You have not indicated what software you are using. However, if you use plspm in the R framework you can use the function rescale() to convert standardised scores into the original scales.

• Thanks. Im using smartPLS to build my model and than the sempls in R to estimate it. I know how to predict the standardized LV scores with my path coeffcients and the other variables. But I have no idea how to predict the unstandardized LV score. Jul 4 '14 at 13:08
• Standardisation only means to substract the mean and divide by the standard deviation ((x-mean)/sd). Just transform your standardised LV score by using the inverse (i.e.: x = Stand.LVScore * SD + mean).
– phx
Jul 4 '14 at 13:14
• Yeah. I know. But I dont know the sd and mean of the unstandardized prediction. I know my StandLV and my unstandLV. But prediction gives me only the StandLV Jul 4 '14 at 13:24
• Just calculate the the unstandardised solutions of your dependent variable using the weights of the responding measurement models and the manifest scores of the indicators as you have described in your question. From this unstandardised score you can derive the mean and the sd for your further calculations. I am not completely sure but that should do...
– phx
Jul 4 '14 at 13:31