Cross Validated Asked by phx on December 1, 2020

I need a generalisable way to to calculate $R^2$ from given regression estimates (regression coefficients, variances of variables, covariances between variables, residual variance of the response variable).

**Detailed problem and question:**

I am estimating a structural equation model with interactions in `Mplus`

. This so called Latent Moderator Analysis is established and works well enough (using the `XWITH`

command in `Mplus`

). However, `Mplus`

is not able to estimate $R^2$ for such models.

Maslowsky, Jager and Hemken (2014, p. 50) argue that one can estimate $R^2$ using a model’s estimated regression coefficients ($beta_{xi}$), variances of the latent predictors ($sigma_{xi}^2$), the covariance(s) between the latent predictors ($sigma_{xij}^2$) as well as the residual variance of the response variable ($sigma_{Yres}^2$).

Unfortunately, the authors present the equation to estimate $R^2$ only for two independent variables (I tested the given equation for a model with two variables and it works fine). I am, however, not able to generalise this equation and to use it with more than two independent variables. Indeed, I need it for four and eventually seven predictors in a regression model.

**How can this equation be generalised to more than two variables?**

In addition, the authors present this equation to estimate the $R^2$ for the model with interactions (p. 50):

**How can this equation be generalised to more than two variables?**

In my case I have four (and eventually with the control variables seven) independent variables and three interaction variables (with a $beta_{xixj}$ each). In other words, one moderator variable moderates three main effects on the response variable.

I would be very grateful for help. Many thanks indeed!

**References**

Maslowsky, J., Jager, J., & Hemken, D. (2015). Estimating and interpreting latent variable interactions: A tutorial for applying the latent moderated structural equations method. *International Journal of Behavioral Development, 39*(1), 87–96. https://doi.org/10.1177/0165025414552301

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