Positive and Negative Q2

Analysis
1

Hi everyone,

I am running a two component PLS model, and I am interested in the Q2 of the individual Y variables (not the average or total Q2 of the model).

My question is: how to interpret results when the Q2 of the first component is positive and the Q2 of the second component is negative; or, when the Q2 of the first component is negative and the Q2 of the second component is positive.

Consider the following four possibilities of Q2 values for a single Y variable in a 2-component PLS model:

|Q2 of Comp1|Q2 of Comp2|
| 0.5 | -0.3 |
| -0.3 | 0.5 |
| 0.3 | -0.5 |
| -0.5 | 0.3 |

Would we consider the model โ€œpredictiveโ€ in any of these situations?

Any insight would be greatly appreciated!

Thank you!

2

hi @bort,
There has been a few discussions about the Q2. Basically (copy pasting from the e-book we are currently preparing):

The ๐‘„^2 criterion is a global measure that applies to both PLS1 and PLS2 and is calculated per dimension h (denoted ๐‘„_h^2). We can decide to retain a dimension h if ๐‘„_h^2 โ‰ฅ 0.975, a (somewhat) arbitrary threshold used in the SIMCA-P software (Umetri, 1996). A negative value of the ๐‘„_h^2 indicates a poor fit of the PLS model on the data.

In your case, going from positive to negative indicates a poor (predictive) fit when you go from dimension 2, or vice versa. It also depends on the type of CV fold you are using, and the number of samples.

You can refer to earlier posts for some details: Q2.total negative in perf.pls

Kim-Anh