COUNT_REGRESSION: Count data regression

Description

Provides SPSS- and SAS-like output for count data regression, including Poisson, quasi-Poisson, negative binomial, zero-inflated poisson, and zero-inflated negative binomial models. The output includes model summaries, classification tables, omnibus tests of the model coefficients, overdispersion tests, model effect sizes, the model coefficients, correlation matrix for the model coefficients, collinearity statistics, and casewise regression diagnostics.

Usage

COUNT_REGRESSION(data, DV, forced = NULL, hierarchical = NULL,
                 family = 'poisson',
                 offset = NULL,
                 plot_type = 'residuals',
                 CI_level = 95,
                 MCMC = FALSE,
                 Nsamples = 4000,
                 verbose = TRUE )

Value

An object of class "COUNT_REGRESSION". The object is a list containing the following possible components:

modelMAIN: All of the glm function output for the regression model.
modelMAINsum: All of the summary.glm function output for the regression model.
modeldata: All of the predictor and outcome raw data that were used in the model, along with regression diagnostic statistics for each case.
collin_diags: Collinearity diagnostic coefficients for models without interaction terms.

Arguments

data

A dataframe where the rows are cases and the columns are the variables.

DV

The name of the dependent variable.
Example: DV = 'outcomeVar'.

forced

(optional) A vector of the names of the predictor variables for a forced/simultaneous entry regression. The variables can be numeric or factors.
Example: forced = c('VarA', 'VarB', 'VarC')

hierarchical

(optional) A list with the names of the predictor variables for each step of a hierarchical regression. The variables can be numeric or factors.
Example: hierarchical = list(step1=c('VarA', 'VarB'), step2=c('VarC', 'VarD'))

family

(optional) The name of the error distribution to be used in the model. The options are:

"poisson" (the default),
"quasipoisson",
"negbin", for negative binomial,
"zinfl_poisson", for zero-inflated poisson, or
"zinfl_negbin", for zero-inflated negative binomial.

Example: family = 'quasipoisson'

offset

(optional) The name of the offset variable, if there is one. This variable should be in the desired metric (e.g., log). No transformation of an offset variable is performed internally.
Example: offset = 'Varname'

plot_type

(optional) The kind of plots, if any. The options are:

'residuals' (the default),
'diagnostics', for regression diagnostics, and
'none', for no plots.

Example: plot_type = 'diagnostics'

CI_level

(optional) The confidence interval for the output, in whole numbers. The default is 95.

MCMC

(logical) Should Bayesian MCMC analyses be conducted? The default is FALSE.

Nsamples

(optional) The number of samples for MCMC analyses. The default is 10000.

verbose

(optional) Should detailed results be displayed in console?
The options are: TRUE (default) or FALSE. If TRUE, plots of residuals are also produced.

Author

Brian P. O'Connor

Details

This function uses the glm function from the stats package, and the negative.binomial function from the MASS package, and supplements the output with additional statistics and in formats that resembles SPSS and SAS output. The predictor variables can be numeric or factors.

The analyses for the zero-inflated poisson and zero-inflated negative binomial analyses are conducted using the pscl package (Zeileis, Kleiber, & Jackman, 2008).

Predicted values, for selected levels of the predictor variables, can be produced and plotted using the PLOT_MODEL funtion in this package.

The Bayesian MCMC analyses can be time-consuming for larger datasets. The MCMC analyses are conducted using functions, and their default settings, from the rstanarm package (Goodrich, Gabry, Ali, & Brilleman, 2024). Family = 'quasibinomial' analyses are currently not possible for the MCMC analyses. family = 'binomial' is therefore used instead. The Bayesian MCMC analyses are also currently not available for zero-inflated poisson and zero-inflated negative binomial models.

The MCMC results can be verified using the model checking functions in the rstanarm package (e.g., Muth, Oravecz, & Gabry, 2018).

Good sources for interpreting count data regression residuals and diagnostics plots:

References

Atkins, D. C., & Gallop, R. J. (2007). Rethinking how family researchers model infrequent outcomes: A tutorial on count regression and zero-inflated models. Journal of Family Psychology, 21(4), 726-735.

Beaujean, A. A., & Grant, M. B. (2019). Tutorial on using regression models with count outcomes using R. Practical Assessment, Research, and Evaluation: Vol. 21, Article 2.

Coxe, S., West, S.G., & Aiken, L.S. (2009). The analysis of count data: A gentle introduction to Poisson regression and its alternatives. Journal of Personality Assessment, 91, 121-136.

Dunn, P. K., & Smyth, G. K. (2018). Generalized linear models with examples in R. Springer.

Hardin, J. W., & Hilbe, J. M. (2007). Generalized linear models and extensions. Stata Press.

Muth, C., Oravecz, Z., & Gabry, J. (2018). User-friendly Bayesian regression modeling: A tutorial with rstanarm and shinystan. The Quantitative Methods for Psychology, 14(2), 99119.
https://doi.org/10.20982/tqmp.14.2.p099

Orme, J. G., & Combs-Orme, T. (2009). Multiple regression with discrete dependent variables. Oxford University Press.

Rindskopf, D. (2023). Generalized linear models. In H. Cooper, M. N. Coutanche, L. M. McMullen, A. T. Panter, D. Rindskopf, & K. J. Sher (Eds.), APA handbook of research methods in psychology: Data analysis and research publication, (2nd ed., pp. 201-218). American Psychological Association.

Zeileis, A., Kleiber, C., & Jackman, S. (2008). Regression Models for Count Data in R. Journal of Statistical Software, 27(8). https://www.jstatsoft.org/v27/i08/.

Examples

Run this code

COUNT_REGRESSION(data=data_Kremelburg_2011, DV='OVRJOYED', 
                 forced=c('AGE','EDUC','REALRINC','SEX_factor'))

COUNT_REGRESSION(data=data_Kremelburg_2011, DV='OVRJOYED', 
                 forced=c('AGE','EDUC','REALRINC','SEX_factor'),  family = 'negbin')

# \donttest{
# negative binomial regression
COUNT_REGRESSION(data=data_Kremelburg_2011, DV='HURTATWK', 
                 forced=c('AGE','EDUC','REALRINC','SEX_factor'),
                 family = 'negbin',
                 plot_type = 'diagnostics')

# with an offset variable
COUNT_REGRESSION(data=data_Orme_2009_5, DV='NumberAdopted', forced=c('Married'), 
                 offset='lnYearsFostered')

# zero-inflated poisson regression
COUNT_REGRESSION(data=data_Kremelburg_2011, DV='HURTATWK', 
                 forced=c('AGE','EDUC','REALRINC','SEX_factor'),
                 family = 'zinfl_poisson',
                 plot_type = 'diagnostics')

# zero-inflated negative binomial regression
COUNT_REGRESSION(data=data_Kremelburg_2011, DV='HURTATWK', 
                 forced=c('AGE','EDUC','REALRINC','SEX_factor'),
                 family = 'zinfl_negbin',
                 plot_type = 'diagnostics')
# }

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