How to decide on the number of factors to be chosen for a PLS regression in case as below
Explained variance (x) - 100% for two factors
Explained variance (y) - 80% for two factors
Explained variance (y) - 98% for seven factors
RMSE reduces as number of factors increase
Dear Mohd,
We never use explained variance in order to select the optimal number of PLS factors.
There are two well-known ways:
1) Cross-validation procedure
2) Test set procedure (if you have a huge data set)
Best regards.
In modelling parametric parsimony is a requirement. R-squared is the percentage of variation explained by the model. If all (i.e. 100%) of the variation in the data is explained by the inclusion of just two variables there is hardly any need to include more variables.
However where R-squared increases with the number of variables included in the model, an order determination criterion like Akaike Information Criterion (AIC) which has an over-parametrization penalty, may be used. For such a statistic minimization is the criterion.
Dear Mohd.
Choosing the number of factors depends on the factor loading as well as the sample size. If sample size is greater than 250, you may set the .40 surplus value of factor loading and if at least two scale items positively loads then you may use that as a construct.
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