Defining the model

Marcello Gallucci

2024-10-14

library(GAMLj3)
data("clustermanymodels")
data<-clustermanymodels

Main model

Model formula

The easiest and recommended way to define a model is to pass a formula. Formula formats accepted by stats:glm and lme4::lmer() functions are accepted.

For instance, a regression with interaction is passed as:

mod1<-gamlj_lm(formula = y~x*z, data=data)

For mixed and generalized mixed models the lme4::lmer() format is accepted:

mod2<-gamlj_lm(formula = y~x*z+(1+x|cluster), data=data)

For logistic models, a part from the standard format, one can pass the formula with two additional format: The first allows passing the counts of successes and the counts of failures as a combined array.

mod3<-gamlj_glm(formula = cbind(success,failure)~x*z, model_type="logistic",data=data)

Alternatively, one can pass the probability of success (with 0≤p≤10\le p \le 1) and the counts of cases (tottot) for each row in the data.frame. The format uses / to indicate p over T.

mod4<-gamlj_glm(formula = p / tot ~x*z, model_type="logistic", data=data)

In all models, polynomial terms can be passed using the I() format:

mod5<-gamlj_lm(formula = y ~x + I(x^2) , data=data)

Please notice that the I() is not interpreted literally, so the term is build after any manipulation of the variable takes places, such as centering or standardizing.

Model terms

Another way to define the model is to define the arguments model_terms and defining the dependent variable with the argument dep. model_terms can be passed as a right-hand formula or as a list.

gamlj_lm(dep=ycont,model_terms=~x*z , data=data)
gamlj_lm(dep=ycont,model_terms=list("x","z",c("x","z")) , data=data)

When terms is passed as a list, each element is a term, and elements with more than 1 term, such as c("x","z") are interactions.

For mixed and generalized mixed models, this method requires to define the random effects of the model with argument re.

For mixed and generalized mixed models, there are also the terms of the comparison model that can be defined as formula:

  • nested_re: define the random coefficients of a nested model to compare.
  • nested_terms: define the random coefficients of a nested model to compare.
gamlj_mixed(formula=ycont~x+(1+x|cluster),nested_terms=~1,nested_re=~1|cluster, data=data)

List of variables

Finally, one can simply specify the factors and the covariates. In this way, however, no higher terms can be defined.

gamlj_lm(dep=ycont,factors=c("cat2"),covs=c("x","z") , data=data)

For mixed and generalized mixed models, this method requires to define the random effects of the model with argument re

Passing other arguments

Several arguments if gamlj_* functions can be passed either as formula or as a list. They are:

  • emmeans: estimate marginal means.
  • posthoc: make post-hoc comparisons.
  • nested_terms: define the terms of a nested model to compare.

For both argument, either a right-hand formula or a list can be passed.

data$cat2<-factor(data$cat2)
data$cat3<-factor(data$cat3)

gamlj_lm(formula=ycont~cat2*cat3,posthoc=~cat2+cat2:cat3 , data=data)

This produces the comparisons only across cat2 levels and the comparison across the interaction cat2*cat3cat2*cat3. For these arguments, we do not use the formula cat2*cat3 because it is not expanded, so passing cat2*cat3 would produce two tables of comparisons, one for the comparison across cat2 levels, and one across cat3 levels.

The equivalent argument as a list is:

gamlj_lm(formula=ycont~cat2*cat3,posthoc=list("cat2",c("cat2","cat3")) , data=data)

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