Estimation of the log Likelihood of the Saturated Model

When the values of the outcome variable Y are either 0 or 1, the function lsm() calculates the estimation of the log likelihood in the saturated model. This model is characterized by Llinas (2006, ISSN:2389-8976) in section 2.3 through the assumptions 1 and 2. The function LogLik() works (almost perfectly) when the number of independent variables K is high, but for small K it calculates wrong values in some cases. For this reason, when Y is dichotomous and the data are grouped in J populations, it is recommended to use the function lsm() because it works very well for all K.

lsm()

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Welcome to the lsm package!

When the values of the outcome variable Y are either 0 or 1, the function calculates the estimation of the log likelihood in the saturated model. This model is characterized by Llinas (2006, ISSN:2389-8976) in section 2.3 through the assumptions 1 and 2. If is dichotomous and the data are grouped in J populations, it is recommended to use the function because it works very well for all .

Details

The saturated model is characterized by the assumptions 1 and 2 presented in section 2.3 by Llinas (2006, ISSN:2389-8976).

Installation

install.packages("lsm")
library(lsm)

Example Usage

Hosmer, D. (2013) page 3: Age and coranary Heart Disease (CHD) Status of 20 subjects:

library(lsm)

  AGE <- c(20,23,24,25,25,26,26,28,28,29,30,30,30,30,30,30,30,32,33,33)
  CHD <- c(0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0)
  
  data <- data.frame (CHD,  AGE )
  lsm(CHD ~ AGE , family=binomial, data)
  
  ## For more ease, use the following notation.
  
  lsm(y~., data)

Other case.

   y <- c(1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1)
  x1 <- c(2, 2, 2, 5, 5, 5, 5, 8, 8, 11, 11, 11)
 
  data <- data.frame (y, x1)
  ELAINYS <-lsm(y ~ x1, family=binomial, data)
  summary(ELAINYS)

Other case.

  y <- as.factor(c(1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1))
  x1 <- as.factor(c(2, 2, 2, 5, 5, 5, 5, 8, 8, 11, 11, 11))
 
  data <- data.frame (y, x1)
  ELAINYS1 <-lsm(y ~ x1, family=binomial, data)
  confint(ELAINYS1)

References

[1] Humberto Jesus Llinas. (2006). Accuracies in the theory of the logistic models. Revista Colombiana De Estadistica,29(2), 242-244.

[2] Hosmer, D. (2013). Wiley Series in Probability and Statistics Ser. : Applied Logistic Regression (3). New York: John Wiley & Sons, Incorporated.

[3] Chambers, J. M. and Hastie, T. J. (1992) Statistical Models in S. Wadsworth & Brooks/Cole.

Author(s)

Humberto Llinas Solano [aut], Universidad del Norte, Barranquilla-Colombia \ Omar Fabregas Cera [aut], Universidad del Norte, Barranquilla-Colombia \ Jorge Villalba Acevedo [cre, aut], Universidad Tecnológica de Bolívar, Cartagena-Colombia.

If you found any ERRORS or have SUGGESTIONS, please report them to my email. Thanks.