lsm2: Estimation of the log Likelihood of the Saturated Model
In jlvia1191/jorge: Estimation of the log Likelihood of the Saturated Model

Description Usage Arguments Details Value Author(s) References Examples

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. If 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.

1	lsm2(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 lsm() is called.

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

Value of the estimation and the total of the population.

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

[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.

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

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)
lsm2(CHD ~ AGE , data)

# Other case.

y	<- c(0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1)
 x1 <- c(2, 2, 2, 2,	2, 5, 5, 5, 5, 6, 6, 6, 8, 8, 11, 11, 11, 1)
 x2 <- c(3, 3, 3, 3,	3, 6,	6, 6, 6, 8, 8, 8, 9, 9, 12,	12,	12,	12)
 x3 <- c(4, 4, 4, 4,	4, 7,	7, 7, 7, 9, 9, 9, 10, 10, 13,	13,	13,	13)
 x4 <- c(1, 1, 1, 1,	1, 9,	9, 9, 9, 10, 10, 10, 4, 4, 2, 2, 2, 2)
 x5 <- c(32, 32, 32, 32, 32, 20, 20, 20, 20, 21, 21, 21, 19, 19, 16, 16, 16, 16)
 x6 <- c(15, 15, 15, 15, 15, 18, 18, 18, 18, 16, 16, 16, 25, 25, 20, 20, 20, 20)
 x7 <- c(28, 28, 28, 28, 28, 23, 23, 23, 23, 32, 32, 32, 24, 24, 32, 32, 32, 32)
 x8 <- c(0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0)
 x9 <- c(6, 6, 6, 6, 6, 10, 10, 10, 10, 11, 11, 11, 7, 7, 21, 21, 21, 21)
 x10 <- c(5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8)

 data <- data.frame (y, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
 lsm2(y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10, data)

## For more ease, use the following notation.
 lsm2(y~., data)

## 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))
 x2 <- as.factor(c(3, 3, 3, 6, 6, 6, 6, 9, 9, 12, 12, 12))
 x3 <- as.factor(c(4, 4, 4, 7, 7, 7, 7, 10, 10, 13, 13, 13))
 x4 <- as.factor(c(1, 1, 1, 9, 9, 9, 9, 4, 4, 2, 2, 2))
 x5 <- as.factor(c(5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8))

 data <- data.frame (y, x1, x2, x3, x4, x5)
 lsm(y ~ x1 + x2 + x3 + x4 + x5, data)

## For more ease, use the following notation.
 lsm(y~., data)