I want to know if my response variable "Ratio" is influenced by 2 fixed factors : "Protection" and "essai" Each experimental units has one level of ESSAI and one level of PROTECTION

I established the following model that best fits my data : gamlss(formula = Ratio ~ ESSAI + PROTECTION, sigma.formula = ~ESSAI,
nu.formula = ~ESSAI, tau.formula = ~ESSAI + (re(random = ~1 |
BRANCHE_NB)), family = BEINF, data = D_tr, trace = FALSE)

The summary of this model gives these estimates for mu :

Mu Coefficients:

        Estimate Std. Error t value Pr(>|t|)    

(Intercept) -0.6092 0.3806 -1.601 0.1140
ESSAI2 0.3542 0.4162 0.851 0.3977
ESSAI3 3.3324 0.3405 9.785 1.13e-14 ***

PROTECTIONG -0.1449 0.4065 -0.357 0.7225
PROTECTIONR -0.6274 0.2838 -2.210 0.0304 *
PROTECTIONT 0.1846 0.2982 0.619 0.5380

I understand that mu estimate for PROTECTION R is significantly different from mu estimate for ESSAI1 (the intercept), but what is the sense of comparing groups by levels of 2 different factors ? Indeed,the experimental units belong to one level of ESSAI and also to one level of PROTECTION.

Also, PROTECTION has 4 levels, so why do summary shows estimates for only 3 of them ?

Thank you in advance


1 Answer 1


The intercept is the fitted value of mu for the first levels of ESSAI and PROTECTION.

PROTECTION-R gives the extra effect on the predictor of mu for R, which is significantly different from zero (using the approximate Wald test).

  • $\begingroup$ Thanks, If I want the mu parameter value for PROTECTIONR, do I have to add the estimate for level R to the intercept ? $\endgroup$ Commented Oct 24, 2023 at 12:34

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