Partial Least Square Regression_Interpretation of Result_VIP_Model Equation_urgentpls

#1
Hello! I would like to ask your help about the interpretation of my results. So I am doing an analysis about which among the environmental predictors (X variables) are the most influential in the coral cover dostribution (Y). I was advised to use partial least regression with the type of data that I have. I used XlStat addin in excel since it is convenient to use.

I hypothesized that Depths, Hs (wave height), and PAR are the most controlling factors based on the Pearson correlation matrix (which showed the greatest correlation with the coral cover). However, when the analysis was done, and showed the model regression equation, the coefficient of SST (sea surface temperature) showed the highest value of coefficient. I was thinking that if you get the highest value for the coefficient, it means that it has the greatest contribution in predicting the Y variable.

Moreover, the variable importance in the prediction (VIP) results, it supported my hypothesis, where depths, Hs, and PAR are the most controlling factor.

So Im a bit confused with the difference of the results, and interpreting this.

I attached the pictures here:


correlation matrix: http://prntscr.com/46i0o3
variable of importance: http://prntscr.com/46i0zi
model equation: http://prntscr.com/46i13p

Thank you very much in advance! It will be great help really, im finishing my analysis for my manuscript, and getting a bit desperate already ;-(
 
#2
Re: Partial Least Square Regression_Interpretation of Result_VIP_Model Equation_urgen

I don't know much about pls. I think of it mainly as a prediction model. Is it also possible to interpret the parameter estimates? I don't know. It is possible to have a variable that is important as used for a prediction variable. That does not necessarily mean that it has a causal influence. For that I think that it would be more interesting with a structural equations model. (Which I don't know much about either :) )
 
#3
Re: Partial Least Square Regression_Interpretation of Result_VIP_Model Equation_urgen

Ms. GretaGarbo, Hello! thanks for your reply! But as I was looking again (for the nth time) on my analysis, I forgot to check the p-values. and it all answer my question. SST should be removed in the model equation as it does not contribute significantly to the changes in Y. I just hope my interpretation is correct.
 
#4
Re: Partial Least Square Regression_Interpretation of Result_VIP_Model Equation_urgen

Can you really do such a conclusion in pls-models?

I thought that the number of factors were determined by cross validation, not the number of variables. Will the estimated variance etc. be correct if such a two stage performance is done? I.e. first selecting variables that are nominally significant in a first test run and then do the cross validation with the "preferred" variables? I don't know. Maybe someone has a suggestion.
 
#5
Re: Partial Least Square Regression_Interpretation of Result_VIP_Model Equation_urgen

Hello, honestly I cant answer that question neither. I was just also hypothesizing here based on looking at the distribution of my environmental variables against coral cover. At least (visually), SST distribution prettily doesn't show any patterns when overlaid to coral cover points. But I have to make sure about this so that's why I need to back it up with statistical analysis. I hope someone can shed some other suggestions too. I actually just need to identify the "most" important variable in the distribution of my Y (coral cover).
 
#6
Re: Partial Least Square Regression_Interpretation of Result_VIP_Model Equation_urgen

Why don't you just do a usual multiple linear regression model? More people would know what you mean with that, thus increasing the communication value.

For "the-most-important-variable issue" I would just look at the parameter estimate judge which on is the most influential/important. Some people standardize both the y-variable and the x-variables and re-estimates and look at which beta estimate is the largest. I am not really a fan of that procedure, but it is often used.
 
#7
Re: Partial Least Square Regression_Interpretation of Result_VIP_Model Equation_urgen

Hello, yes, ive tried that, but it gives really obvious weird results. The problem with my predictors (X variables) is that some have high collinearity, that's why I was advised to use PLS.