Fitting Generalized Linear Models with Abundance-Based Constraints (ABCs)

glmabc is used to fit generalized linear models using abundance-based constraints (ABCs). Like stats::glm, the model is specified by giving a symbolic description of the linear predictor and a description of the error distribution. ABCs provide more equitable and interpretable output for regression models with categorical covariates.

Usage

glmabc(formula, family = stats::gaussian, data, props = NULL)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under ‘Details’.

family

a description of the error distribution and link function to be used in the model. For glm this can be a character string naming a family function, a family function or the result of a call to a family function. For glm.fit only the third option is supported. (See family for details of family functions.)

data

an optional data frame (or object coercible by as.data.frame to a data frame) containing the variables in the model.

props

an optional named list with an entry for each named categorical variable in the model, specifying the proportions of each category. By default, props will be calculated from the empirical proportions in the data.

Details

A glmabc model is specified identically to the corresponding glm model. At this time, glmabc only supports a single response variable.

See lmabc() for details and motivation about ABCs for categorical covariates. Note that the ABCs estimation/inference invariance properties no longer apply for GLMs, but the arguments for equitability and interpretability remain valid.

Value

glmabc returns an object of classes "glmabc" and "lmabc." Many generics commonly used for glm objects have been implemented for glmabc: summary, coefficients, plot, predict, and more. See the DESCRIPTION file for all implemented S3 methods.

See also

stats::glm() for the standard generalized linear regression implementation in R.

Examples

mtcars$cyl <- as.factor(mtcars$cyl)
fit <- glmabc(am ~ mpg + cyl + mpg:cyl, family = "binomial", data = mtcars)
summary(fit)
#> 
#> Call:
#> glmabc(formula = am ~ mpg + cyl + mpg:cyl, family = "binomial", 
#>     data = mtcars)
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -1.13572    0.91699  -1.239    0.227
#> mpg          0.40528    0.24936   1.625    0.116
#> cyl4        -0.18919    1.23255  -0.153    0.879
#> cyl6         1.03642    1.14001   0.909    0.372
#> cyl8        -0.36956    1.09408  -0.338    0.738
#> mpg:cyl4     0.07703    0.31668   0.243    0.810
#> mpg:cyl6     0.57172    0.62998   0.908    0.372
#> mpg:cyl8    -0.34638    0.27347  -1.267    0.217
#> 
#> (Dispersion parameter for binomial family taken to be 1)
#> 
#>     Null deviance: 43.230  on 31  degrees of freedom
#> Residual deviance: 27.676  on 26  degrees of freedom
#> AIC: 39.676
#> 
#> Number of Fisher Scoring iterations: 6
#> 

predict(fit, newdata = data.frame(mpg = 21, cyl = "6"), type = 'response')
#>         1 
#> 0.6876515