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glsm()
When the response variable Y takes one of R > 1 values, the function ‘glsm()’ computes the maximum likelihood estimates (MLEs) of the parameters under four models: null, complete, saturated, and logistic. It also calculates the log-likelihood values for each model. This method assumes independent, non-identically distributed variables. For grouped data with a multinomial outcome, where observations are divided into J populations, the function ‘glsm()’ provides estimation for any number K of explanatory variables.
The saturated model is characterized by the assumptions 1 and 2 presented in section 2.3 by Llinás (2006).
You can install the development version of glsm like so:
# install.packages("devtools")
remotes::install_github("jlvia1191/glsm", force = TRUE)
devtools::install_github("jlvia1191/glsm", force = TRUE)This is a basic example which shows you how to solve a common problem:
library(glsm)
data("hsbdemo", package = "glsm")
model <- glsm(prog ~ ses + gender, data = hsbdemo, ref = "academic")
model
#>
#> Call:
#> glsm(formula = prog ~ ses + gender, data = hsbdemo, ref = "academic")
#>
#> Populations in Saturated Model: 6
#>
#> Coefficients:
#> Coef(B) Std.Error
#> (Intercept):general -1.6547758 0.4175354
#> (Intercept):vocation -1.8469099 0.4478055
#> seslow:general 1.4118732 0.5064763
#> seslow:vocation 1.3534875 0.5548849
#> sesmiddle:general 0.7550865 0.4561360
#> sesmiddle:vocation 1.4430949 0.4709456
#> gendermale:general 0.2216624 0.3716764
#> gendermale:vocation 0.1098969 0.3599743
#> Exp(B)
#> (Intercept):general 0.1911349
#> (Intercept):vocation 0.1577238
#> seslow:general 4.1036349
#> seslow:vocation 3.8709018
#> sesmiddle:general 2.1277956
#> sesmiddle:vocation 4.2337787
#> gendermale:general 1.2481500
#> gendermale:vocation 1.1161630
#>
#> Log Likelihood:
#> Estimation
#> Complete 0.0000
#> Null -204.0967
#> Logit -195.5208
#> Saturate -194.5159[1] Hosmer, D., Lemeshow, S., & Sturdivant, R. (2013). Applied Logistic Regression (3rd ed.). New York: Wiley. ISBN: 978-0-470-58247-3
[2] Llinás, H. (2006). Precisiones en la teoría de los modelos logísticos. Revista Colombiana de Estadística, 29(2), 239–265.
[3] Llinás, H., & Carreño, C. (2012). The Multinomial Logistic Model for the Case in Which the Response Variable Can Assume One of Three Levels and Related Models. Revista Colombiana de Estadística, 35(1), 131–138.
[4] Orozco, E., Llinás, H., & Fonseca, J. (2020). Convergence theorems in multinomial saturated and logistic models. Revista Colombiana de Estadística, 43(2), 211–231.
[5] Llinás, H., Arteta, M., & Tilano, J. (2016). El modelo de regresión logística para el caso en que la variable de respuesta puede asumir uno de tres niveles: estimaciones, pruebas de hipótesis y selección de modelos. Revista de Matemática: Teoría y Aplicaciones, 23(1), 173–197.
Jorge Luis Villalba Acevedo [cre, aut], Universidad Tecnológica de Bolívar, Cartagena-Colombia.\ Humberto Llinas Solano [aut], Universidad del Norte, Barranquilla-Colombia \ Jorge Borja [aut], Universidad del Norte, Barranquilla-Colombia \ Jorge Tilano [aut], Universidad del Norte, Barranquilla-Colombia.
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