loglin {stats}  R Documentation 
loglin
is used to fit loglinear models to multidimensional
contingency tables by Iterative Proportional Fitting.
loglin(table, margin, start = rep(1, length(table)), fit = FALSE, eps = 0.1, iter = 20, param = FALSE, print = TRUE)
table 
a contingency table to be fit, typically the output from
table . 
margin 
a list of vectors with the marginal totals to be fit.
(Hierarchical) loglinear models can be specified in terms of these marginal totals which give the “maximal” factor subsets contained in the model. For example, in a threefactor model, list(c(1, 2), c(1, 3)) specifies a model which contains
parameters for the grand mean, each factor, and the 12 and 13
interactions, respectively (but no 23 or 123 interaction), i.e.,
a model where factors 2 and 3 are independent conditional on factor
1 (sometimes represented as ‘[12][13]’).
The names of factors (i.e., names(dimnames(table)) ) may be
used rather than numeric indices.

start 
a starting estimate for the fitted table. This optional
argument is important for incomplete tables with structural zeros
in table which should be preserved in the fit. In this
case, the corresponding entries in start should be zero and
the others can be taken as one. 
fit 
a logical indicating whether the fitted values should be returned. 
eps 
maximum deviation allowed between observed and fitted margins. 
iter 
maximum number of iterations. 
param 
a logical indicating whether the parameter values should be returned. 
print 
a logical. If TRUE , the number of iterations and
the final deviation are printed. 
The Iterative Proportional Fitting algorithm as presented in
Haberman (1972) is used for fitting the model. At most iter
iterations are performed, convergence is taken to occur when the
maximum deviation between observed and fitted margins is less than
eps
. All internal computations are done in double precision;
there is no limit on the number of factors (the dimension of the
table) in the model.
Assuming that there are no structural zeros, both the Likelihood
Ratio Test and Pearson test statistics have an asymptotic chisquared
distribution with df
degrees of freedom.
Package MASS contains loglm
, a frontend to loglin
which allows the loglinear model to be specified and fitted in a
formulabased manner similar to that of other fitting functions such
as lm
or glm
.
A list with the following components.
lrt 
the Likelihood Ratio Test statistic. 
pearson 
the Pearson test statistic (Xsquared). 
df 
the degrees of freedom for the fitted model. There is no adjustment for structural zeros. 
margin 
list of the margins that were fit. Basically the same
as the input margin , but with numbers replaced by names
where possible. 
fit 
An array like table containing the fitted values.
Only returned if fit is TRUE . 
param 
A list containing the estimated parameters of the
model. The “standard” constraints of zero marginal sums
(e.g., zero row and column sums for a two factor parameter) are
employed. Only returned if param is TRUE . 
Kurt Hornik
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Haberman, S. J. (1972) Loglinear fit for contingency tables—Algorithm AS51. Applied Statistics, 21, 218–225.
Agresti, A. (1990) Categorical data analysis. New York: Wiley.
loglm
in package MASS for a userfriendly wrapper.
glm
for another way to fit loglinear models.
## Model of joint independence of sex from hair and eye color. fm < loglin(HairEyeColor, list(c(1, 2), c(1, 3), c(2, 3))) fm 1  pchisq(fm$lrt, fm$df) ## Model with no threefactor interactions fits well.