# loglin

##### Fitting Log-Linear Models

`loglin`

is used to fit log-linear models to multidimensional
contingency tables by Iterative Proportional Fitting.

##### Usage

```
loglin(table, margin, start = rep(1, length(table)), fit = FALSE,
eps = 0.1, iter = 20, param = FALSE, print = TRUE)
```

##### Arguments

- 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) log-linear models can be specified in terms of these marginal totals which give the

maximal factor subsets contained in the model. For example, in a three-factor model,`list(c(1, 2), c(1, 3))`

specifies a model which contains parameters for the grand mean, each factor, and the 1-2 and 1-3 interactions, respectively (but no 2-3 or 1-2-3 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.
- a logical. If
`TRUE`

, the number of iterations and the final deviation are printed.

##### Details

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 chi-squared
distribution with `df`

degrees of freedom.

Note that the IPF steps are applied to the factors in the order given
in `margin`

. Hence if the model is decomposable and the order
given in `margin`

is a running intersection property ordering
then IPF will converge in one iteration.

Package `loglm`

, a front-end to
`loglin`

which allows the log-linear model to be specified and
fitted in a formula-based manner similar to that of other fitting
functions such as `lm`

or `glm`

.

##### Value

- A list with the following components.
lrt the Likelihood Ratio Test statistic. pearson the Pearson test statistic (X-squared). 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`

.

##### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth & Brooks/Cole.

Haberman, S. J. (1972)
Log-linear fit for contingency tables---Algorithm AS51.
*Applied Statistics*, **21**, 218--225.

Agresti, A. (1990)
*Categorical data analysis*.
New York: Wiley.

##### See Also

`loglm`

in package

`glm`

for another way to fit log-linear models.

##### Examples

`library(stats)`

```
## 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 three-factor interactions fits well.
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*