Fit Log-Linear Models by Iterative Proportional Scaling
This function provides a front-end to the standard function,
loglin, to allow log-linear models to be specified and fitted
in a manner similar to that of other fitting functions, such as
glm.
loglm(formula, data, subset, na.action, ...)
formula |
A linear model formula specifying the log-linear model. If the left-hand side is empty, the |
data |
Numeric array or data frame (or list or environment). In the first case it specifies the array of frequencies; in the second it provides the data frame from which the variables occurring in the formula are preferentially obtained in the usual way. This argument may be the result of a call to |
subset |
Specifies a subset of the rows in the data frame to be used. The default is to take all rows. |
na.action |
Specifies a method for handling missing observations. The default is to fail if missing values are present. |
... |
May supply other arguments to the function |
If the left-hand side of the formula is empty the data argument
supplies the frequency array and the right-hand side of the
formula is used to construct the list of fixed faces as required
by loglin. Structural zeros may be specified by giving a
start argument with those entries set to zero, as described in
the help information for loglin.
If the left-hand side is not empty, all variables on the
right-hand side are regarded as classifying factors and an array
of frequencies is constructed. If some cells in the complete
array are not specified they are treated as structural zeros.
The right-hand side of the formula is again used to construct the
list of faces on which the observed and fitted totals must agree,
as required by loglin. Hence terms such as
a:b, a*b and a/b are all equivalent.
An object of class "loglm" conveying the results of the fitted
log-linear model. Methods exist for the generic functions print,
summary, deviance, fitted, coef,
resid, anova and update, which perform the expected
tasks. Only log-likelihood ratio tests are allowed using anova.
The deviance is simply an alternative name for the log-likelihood ratio statistic for testing the current model within a saturated model, in accordance with standard usage in generalized linear models.
If structural zeros are present, the calculation of degrees of
freedom may not be correct. loglin itself takes no action to
allow for structural zeros. loglm deducts one degree of
freedom for each structural zero, but cannot make allowance for
gains in error degrees of freedom due to loss of dimension in the
model space. (This would require checking the rank of the
model matrix, but since iterative proportional scaling methods
are developed largely to avoid constructing the model matrix
explicitly, the computation is at least difficult.)
When structural zeros (or zero fitted values) are present the estimated coefficients will not be available due to infinite estimates. The deviances will normally continue to be correct, though.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
# The data frames Cars93, minn38 and quine are available # in the MASS package. # Case 1: frequencies specified as an array. sapply(minn38, function(x) length(levels(x))) ## hs phs fol sex f ## 3 4 7 2 0 ##minn38a <- array(0, c(3,4,7,2), lapply(minn38[, -5], levels)) ##minn38a[data.matrix(minn38[,-5])] <- minn38$f ## or more simply minn38a <- xtabs(f ~ ., minn38) fm <- loglm(~ 1 + 2 + 3 + 4, minn38a) # numerals as names. deviance(fm) ## [1] 3711.9 fm1 <- update(fm, .~.^2) fm2 <- update(fm, .~.^3, print = TRUE) ## 5 iterations: deviation 0.075 anova(fm, fm1, fm2) # Case 1. An array generated with xtabs. loglm(~ Type + Origin, xtabs(~ Type + Origin, Cars93)) # Case 2. Frequencies given as a vector in a data frame names(quine) ## [1] "Eth" "Sex" "Age" "Lrn" "Days" fm <- loglm(Days ~ .^2, quine) gm <- glm(Days ~ .^2, poisson, quine) # check glm. c(deviance(fm), deviance(gm)) # deviances agree ## [1] 1368.7 1368.7 c(fm$df, gm$df) # resid df do not! c(fm$df, gm$df.residual) # resid df do not! ## [1] 127 128 # The loglm residual degrees of freedom is wrong because of # a non-detectable redundancy in the model matrix.
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