stepwiseglm model seems to be missing parameters?

In below, stepwiseglm produces a model without x1 and x2, but does not seem to be removing those during steps, and also gives estimates for their coefficients with proper pValue.

Is the model correct? If so, why are x1 and x2 not visible? In the same script, also two other models are produced, but they do include x1 and/or x2 in model, as appropriate.

g2 = stepwiseglm([Pplay,Lplay],(1/6)*DData(:,1),...
    'Poly55','Lower','constant','Upper','Poly55','Distribution','Normal','link','probit');
    g2
    
    
        1. Removing x1^5, Deviance = 0.26439, FStat = NaN, PValue = NaN
        2. Removing (x1^4):x2, Deviance = 0.26439, FStat = NaN, PValue = NaN
        3. Removing x1^4, Deviance = 0.26439, FStat = NaN, PValue = NaN
        4. Removing (x1^3):(x2^2), Deviance = 0.26439, FStat = NaN, PValue = NaN
        5. Removing (x1^3):x2, Deviance = 0.26439, FStat = NaN, PValue = NaN
        6. Removing x1^3, Deviance = 0.26439, FStat = Inf, PValue = NaN
        7. Removing (x1^2):(x2^3), Deviance = 0.26439, FStat = NaN, PValue = NaN
        8. Removing (x1^2):(x2^2), Deviance = 0.26439, FStat = NaN, PValue = NaN
        9. Removing (x1^2):x2, Deviance = 0.26439, FStat = NaN, PValue = NaN
        10. Removing x1:(x2^4), Deviance = 0.26439, FStat = Inf, PValue = NaN
        11. Removing x2^5, Deviance = 0.27142, FStat = 0.34533, PValue = 0.56684
        12. Removing x1^2, Deviance = 0.30183, FStat = 1.5689, PValue = 0.23089
        
        g2 = 
        Generalized linear regression model:
        probit(y) ~ 1 + x1*x2 + x2^2 + x1:(x2^2) + x2^3 + x1:(x2^3) + x2^4
        Distribution = Normal
        
        Estimated Coefficients:
        Estimate          SE         tStat      pValue 
        ___________    __________    _______    ________
        
        (Intercept)        -34.094        14.351    -2.3757    0.031276
        x1                   14692        5473.4     2.6842    0.016989
        x2                  -12245        5477.9    -2.2354    0.041019
        x1:x2          -6.8006e+05    2.5664e+05    -2.6499    0.018196
        x2^2            6.1705e+05    2.5588e+05     2.4115    0.029161
        x1:x2^2         1.0401e+07    3.9814e+06     2.6124    0.019609
        x2^3           -9.7049e+06    3.9728e+06    -2.4428    0.027425
        x1:x2^3        -5.2558e+07    2.0434e+07    -2.5721    0.021248
        x2^4            4.9767e+07    2.0411e+07     2.4382    0.027675
        
        
        24 observations, 15 error degrees of freedom
        Estimated Dispersion: 0.0201
        F-statistic vs. constant model: 2.89, p-value = 0.0364

Answer 1

[Ive J]

It does include both. You should mind the model formula in MATLAB (AKA Wilkinson Notation): x1*x2 is x1 + x2 + x1:x2.

See also here:

mathworks.com/help/releases/R2021b/stats/wilkinson-notation.html

[Tomi Ylikorpi]

Ah, thanks a lot! Absolutely explains the issue. :)