1. ## noramlization

I weighted the variables to do structural equation modeling (SEM). I found that some weighted variables were not normally distributed. Do I have to normalize the weighted variables before I implement the statistical analysis? Or I don't have to normalize the weighted variables? Thanks.

2. ## Re: noramlization

I does not seem that you are using term "normalize" correctly. Please elaborate.

3. ## Re: noramlization

Normalization means adjustments of values or distributions in statistics. The skewness and kurtosis for nonnormal weighted variables are outside the values range of -1 through +1. I want to use rank transformation to transform nonnormal variables into normal variables so that the skewness and kurtosis for nonnormal weighted varaiables are inside the values range of -1 through +1. . But I am not sure if it's right to normalize the weighted variables by using rank transformation. The process of weighting involves emphasizing the contribution of some aspects of a phenomenon (or of a set of data) to a final effect or result, giving them more weight in the analysis. That is, rather than each variable in the data contributing equally to the final result, some data are adjusted to contribute more than others. Do they imply they are already normally distributed? Or not?

4. ## Re: noramlization

I'm afraid, this is not correct. Quite counterintuitively, "normalization" means subtracting the mean and dividing by the standard deviation. What you are referring to is non-linear transformations.

I do not know under which specifications you run SEM. But even if you choose the option assuming normal distributions of the relevant variables (which you do not have to), the situation is the following. If the sample size is very large relative to the number of parameters, you do not have to apply non-linear transformations to make the variables normal. The SEM tests are still valid... If the sample size is not very large relative to the number of parameters, you should look into the residuals of the linear/non-linear models which are links in the SEM map. If the residuals exhibit non-normality, you have to transform. You can use parametric transformations (Box-Cox for example), semi-parametric transformations (kernel smoothing) or non-parametric transformations (empirical distribution function). The parametric approach is easiest.

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