Linear Mixed Models: how to interpret intercept from multiple fixed factors?

Question

I am running this model using lme4:

RT4.model = glmer(RTs ~ conditionStimuli + sequenceTrials + (conditionStimuli + sequenceTrials || Num_part)
                   , data = data_RTs_go
                   , family=inverse.gaussian(link="identity")
                   , control=glmerControl(optimizer="bobyqa"
                                          , optCtrl=list(maxfun=1e6))
)

conditionStimuli has 3 levels, while sequenceTrials has 2 levels.

When I run the summary() function I obtain this:

Fixed effects:
                       Estimate Std. Error t value Pr(>|z|)    
(Intercept)             491.549      7.704  63.803  < 2e-16 ***
conditionStimulishapes  -31.780      6.404  -4.962 6.96e-07 ***
conditionStimulileaves  -27.639      7.659  -3.609 0.000307 ***
sequenceTrialsNGG        15.794      4.808   3.285 0.001020 ** 

How do I interpret the (Intercept), given that (I suppose) is obtained using one level of conditionStimuli and one of SequenceTrials? Is it interesting/useful to interpret? Regarding random effects, I describe precisely the structure of the model, do I have to report the values of the random effects as well?

Then, I use the car::Anova and emmeans functions to obtain the estimates and p value for the fixed effects.

Thank you,

here is an example of the data:

Num_part trial_type  Go_type conditionStimuli ITI_ms response RTs correctResponse order_pres sequenceTrials sdt
2        1         Go     Bent           leaves    819        1 301               1          1            NGG   1
3        1         Go     Bent           leaves    771        1 237               1          1             GG   1
4        1         Go     Bent           leaves   1086        1 393               1          1             GG   1
5        1         Go Straight           leaves    652        1 331               1          1             GG   1
7        1         Go     Bent           leaves    919        1 372               1          1            NGG   1
9        1         Go Straight           leaves    802        1 359               1          1            NGG   1

Answer 1

With default treatment/dummy coding of categorical predictors, an intercept is just the value of the linear predictor when all categorical predictors are at reference levels and all continuous predictors have 0 values. So if that's an interesting or useful scenario for your data, it would be interesting or useful to interpret it.* The coefficients and p-values for other levels of categorical predictors are for differences from the intercept value.

Rather than focus on any of the individual model coefficients, intercept or otherwise, it's generally best to use tools like those in emmeans to evaluate particular scenarios of interest and the significance of differences among them. That way you make sure that you are handling all the coefficients and their (co)variances properly to get both point estimates and standard errors. That's particularly true when models include interaction terms.

If random effects are an important part of your model then you should report them.

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*The p-value for the intercept is with respect to a null hypothesis that it equals 0. That isn't always an interesting null hypothesis.