R: Generally-Altered Binomial Regression Family Function...

gabinomial.mlm {VGAM}

R Documentation

Generally-Altered Binomial Regression Family Function (multinomial logit model based; GA-binom-MLM)

Description

Fits a generally-altered binomial regression (using a multinomial logit model for the altered values).

Usage

gabinomial.mlm(alter = 0, zero = NULL, lprob = "logitlink", 
    type.fitted = c("mean", "prob", "pobs.a", "Pobs.a"),
    imethod = 1, iprob = NULL)

Arguments

`alter`	Vector of altered values, i.e., nonnegative integers. Must have unique values only. May be a `NULL`, which stands for empty set (same as `binomialff`). The default is the 0-altered binomial
`lprob`	See `Links` for more choices and information.
`type.fitted`	See `CommonVGAMffArguments` for information. The choice `"pobs.a"` is the probability of an altered value. See `gaitpoisson.mlm` for more details.
`imethod, iprob`	See `CommonVGAMffArguments` for information.

zero

See CommonVGAMffArguments for information. Setting zero = "pobs" will model the multinomial probabilities as simple as possible (intercept-only), hence should be more numerically stable than the default, and this is recommended for many analyses especially when there are many explanatory variables..

Details

The generally-altered binomial distribution is the ordinary binomial distribution with the probability of certain values (alter argument) being modelled using a multinomial logit model. The other values are modelled using a generally-truncated binomial distribution. The 0-altered binomial distribution is a special case and is the default (it is called a hurdle model by some people).

This function implements Fisher scoring and currently does not handle multiple responses. Compared to gibinomial (not complete yet) this family function handles deflation and inflation, therefore handles a wider range of data.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

The fitted.values slot of the fitted object, which should be extracted by the generic function fitted, returns the mean mu (default). The choice type.fitted = "pobs.a" returns the sum of all the altered probabilities. See gaitpoisson.mlm for more details.

Note

This family function does not yet have the robustness of multinomial when computing the working weight matrices. Several improvements are needed, e.g., better labelling and initial values and handling multiple responses.

The default value of zero is not the best for most data sets; so assign it a value (see above).

This family function effectively combines gtbinomial and multinomial into one family function.

Author(s)

T. W. Yee and Chenchen Ma

Examples

avec <- c(0, 5)  # Alter these values
Size <- 10
gdata <- data.frame(x2 = runif(nn <- 1000))
gdata <- transform(gdata, x3 = runif(nn))
gdata <- transform(gdata,
           prob1 = logitlink(1 + 2 * x2 + .5 * x3, inverse = TRUE),
           prob2 = logitlink(1 - 1 * x2 + .5 * x3, inverse = TRUE),
           prob3 = logitlink(1, inverse = TRUE))
gdata <- transform(gdata,
  y1 = rgaitbinom.mlm(nn, prob = prob1, Size, pobs.a = c(0.2, 0.3),
                      byrow = TRUE, alter = avec),
  y2 = rgaitbinom.mlm(nn, prob = prob2, Size, pobs.a = c(0.2, 0.3),
                      byrow = TRUE, alter = avec),
  y3 = rgaitbinom.mlm(nn, prob = prob3, Size, pobs.a = c(0.2, 0.3),
                      byrow = TRUE, alter = avec))
gabinomial.mlm(alter = avec)
with(gdata, table(y1))
with(gdata, table(y2))
with(gdata, table(y3))

fit1 <- vglm(cbind(y1, Size-y1) ~ x2 + x3, gabinomial.mlm(alter = avec),
             crit = "coef", trace = TRUE, data = gdata)
head(fitted(fit1))
head(predict(fit1))
coef(fit1, matrix = TRUE)
summary(fit1)

# Another example ------------------------------
fit3 <- vglm(cbind(y3, Size-y3) ~ 1, gabinomial.mlm(alter = avec),
             gdata, trace = TRUE)
coef(fit3, matrix = TRUE)

[Package VGAM version 1.1-3 Index]