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I've made the gam in the code below (in R), but I'm struggling to interpret the results. Specifically, the partial response plots for all but one of the variables is linear, and the CI lines cross in the middle. I've done some looking around and can't find out what this means.

Given these plots, is this model valid? Is there something wrong with the model? If so, how would I make a correction?

Here's the partial response plots:

Partial response plots of the gam

the output figures of gam.check (the residuals passed a normality check, just fyi)

gam.check outputs

and the model code with a summary()

cpue.GAM <- gam(CPUE ~
                  s(CHL) + 
                  s(BEUTI) + 
                  s(PDO) + 
                  s(SST) + 
                  s(HCI) + 
                  s(ONI) + 
                  s(NPP),
                data = master2,
                method = "REML")

> summary(cpue.GAM)

Family: gaussian 
Link function: identity 

Formula:
CPUE ~ s(CHL) + s(BEUTI) + s(PDO) + s(SST) + s(HCI) + s(ONI) + 
    s(NPP)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   5.7861     0.2406   24.05   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
           edf Ref.df      F p-value    
s(CHL)   1.000  1.000  2.985 0.08964 .  
s(BEUTI) 1.000  1.000 12.379 0.00088 ***
s(PDO)   1.000  1.000  0.788 0.37868    
s(SST)   1.000  1.000  6.543 0.01331 *  
s(HCI)   2.021  2.564  2.104 0.10650    
s(ONI)   1.000  1.000  3.901 0.05327 .  
s(NPP)   1.000  1.000  1.499 0.22603    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.337   Deviance explained = 42.1%
-REML = 132.26  Scale est. = 3.7038    n = 64
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  • 1
    $\begingroup$ The main issue is that your model is way too complex for the small number of observations you have. Even if you had fit a purely linear model instead of a GAM, I would say this. Also, have you checked for multicollinearity? $\endgroup$
    – Roland
    Commented May 31, 2023 at 6:23
  • 1
    $\begingroup$ I believe the CI lines cross because the smoothers are centered. $\endgroup$
    – Roland
    Commented May 31, 2023 at 6:24
  • $\begingroup$ Thanks for the help Roland! Yes I did a check for multicollinearity, 2 were collinear so I removed the one that was the least important biologically. The full model originally had more variables, but I reduced model complexity by forward stepwise selection. I've tried setting select = T to reduce the number of variables internally, but that reduced model fit (deviance explained) by 10% and didn't solve the linear figures w/ crossing CI lines issue. I'll try reducing model complexity manually and see what happens. $\endgroup$
    – blitz1259
    Commented May 31, 2023 at 7:31

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