# Scaling after Principal Component Analysis

I am attempting to model the yield of various crops as a function of weather data, namely one temperature variable and 7 moisture-related variables (measuring different aspects of moisture content). The moisture readings exhibited a significant degree of collinearity and were all using different units, and so as recommended by some other answers on this site, I scaled the moisture variables and applied Principal Component Analysis, picking the PCs that accounted for > 95% of the variance cumulatively.

However, I now have a question regarding when to scale the data prior to applying machine learning techniques. I'm trying to build a mixed effects model with lmer in lme4 package. Since the PCs were obtained by scaling only the moisture data, if I wanted to make a model of the form yield ~ temperature + PC1 +... + PCN + (1|categorical vars), would I need to re-scale the dataset consisting of temperature, PC1,...,PCN?

Also, is it recommended to scale the response variable as well? Any clarification and help would be much appreciated; I'm only just getting started on this path.

• Scaling your variables should have no impact on your ability to predict the target variable. The only use I see in your case is in the case of interpreting your model co-efficients. If you were to uniformly scale your independent variables then the model co-efficients can be used to compare which of your factors have a stronger relationship with your target. – Arun Jose Jul 12 '16 at 10:19
• Thank you very much! That put to rest some doubts I had. A follow up question: are there better measures of Goodness-of-fit for mixed effects models other than Root Mean Square Error? And are there any assumptions that the residuals of a mixed-effect model need to follow? – Ananth Ravi Kumar Jul 12 '16 at 11:23

Re-scaling is not necessary and won't affect your model's predictions, unless the data are on such wildly different scales that the model struggles to converge (in which case lmer would produce warning messages)