dsm: Estimation of the log likelihood of the saturated model
In jlvia1191/dsm: Estimation of the log likelihood of the saturated model

Description Usage Arguments Details Value Author(s) References Examples

View source: R/dsm.R

This package calculates the estimation of the log likelihood of the saturated model, when the values of the outcome variable are either 0 or 1.

1	dsm(formula, data)

`formula`	An expression of the form y ~ model, where y is the outcome variable (binary or dichotomous: its values are 0 or 1).
`data`	an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which dsm is called.

The saturated model is characterized by the assumptions 1 and 2 presented in section 5 by Llinas [1]. The variable of interest Y can asume 2 levels 0 or 1. We define P_j:= P(Y=1| j) the probability that Y takes the value of 1 in the population j=1, .J. Taking into account the annotations n_j (size of the population j) and Z_j (number of success in the population j), introduced in that paper, in the saturated model, the ML-estimations of P_j are Z_j/n_j. Furthermore, the logarithm of the function of maximum likelihood would be L(P) =Sum (from j=1 to J) of [Z_j ln P_j + (n_j - Z_j) ln(1 - P_j)], where P=(P_1, ..P_J). It is also fulfilled that L(P) < 0 for 0 <P_j < 1.

Value of the estimation.

Humberto Llinas [aut, cre], Universidad del Norte, Barranquilla-Colombia \ Jorge Villalba [cre], Unicolombo, Cartagena-Colombia \ Omar Fabregas [cre], Universidad del Norte, Barranquilla-Colombia.

LLINAS H., Precisiones en la teoria de modelos logisticos. Revista Colombiana de Estadistica, vol. 29, No. 2, pp. 293-265, 2006.

 x1 <- c(68, 72, 68, 76, 69, 71, 68, 61, 69, 68)
 x2 <- c(0.00, 55.90, 0.00, 20.00, 55.90, 0.00, 27.20, 24.00, 0.00, 27.20)
 y <- c (0, 1, 0, 0, 1, 0, 0, 1, 0, 1)
 data <- data.frame (y, x1, x2)
 dsm(y~x1+x2, data)