# Model comparison for glms.

### Description

A method for the `anova`

function, for use on `svyglm`

objects. With a single model argument it produces a sequential anova table, with two arguments it compares the two models.

### Usage

1 2 3 4 5 6 7 |

### Arguments

`object` |
A |

`object2` |
Optionally, another |

`test` |
Use (linear combination of) F or chi-squared distributions for p-values. F is usually preferable. |

`method` |
Use weighted deviance difference (LRT) or Wald tests to compare models |

`tolerance` |
For models that are not symbolically nested, the tolerance for deciding that a term is common to the models. |

`...` |
For |

`force` |
Force the tests to be done by explicit projection even if the models are symbolically nested (for debugging) |

`maximal` |
A |

`k` |
Multiplier for effective df in AIC. Usually 2. There is no choice of |

### Details

The reference distribution for the LRT depends on the misspecification effects for the parameters being tested (Rao and Scott, 1984). If the models are symbolically nested, so that the relevant parameters can be identified just by manipulating the model formulas, `anova`

is equivalent to `regTermTest`

. If the models are nested but not symbolically nested, more computation using the design matrices is needed to determine the projection matrix on to the parameters being tested. Typical examples of models that are nested but not symbolically nested are linear and spline models for a continuous covariate or linear and saturated models for a factor.

The saddlepoint approximation is used for the LRT with numerator df greater than 1.

`AIC`

is defined using the Rao-Scott approximation to the weighted loglikelihood. It replaces the usual penalty term p, which is the null expectation of the log likelihood ratio, by the trace of the generalised design effect matrix, which is the expectation under complex sampling. For computational reasons everything is scaled so the weights sum to the sample size.

`BIC`

is a BIC for the (approximate) multivariate Gaussian models on regression coefficients from the maximal model implied by each submodel (ie, the models that say some coefficients in the maximal model are zero). It corresponds to comparing the models with a Wald test and replacing the sample size in the penalty by an effective sample size.
For computational reasons, the models must not only be nested, the names of the coefficients must match.

### Value

Object of class `seqanova.svyglm`

if one model is given, otherwise of class `regTermTest`

or `regTermTestLRT`

### Note

At the moment, `AIC`

works only for models including an intercept.

### References

Rao, JNK, Scott, AJ (1984) "On Chi-squared Tests For Multiway Contingency Tables with Proportions Estimated From Survey Data" Annals of Statistics 12:46-60.

Lumley, T., & Scott, A. (2014). Tests for Regression Models Fitted to Survey Data. Australian and New Zealand Journal of Statistics, 56 (1), 1-14.

Lumley T, Scott AJ (forthcoming) "AIC and BIC for modelling with complex survey data"

### See Also

`regTermTest`

, `pchisqsum`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
data(api)
dclus2<-svydesign(id=~dnum+snum, weights=~pw, data=apiclus2)
model0<-svyglm(I(sch.wide=="Yes")~ell+meals+mobility, design=dclus2, family=quasibinomial())
model1<-svyglm(I(sch.wide=="Yes")~ell+meals+mobility+as.numeric(stype),
design=dclus2, family=quasibinomial())
model2<-svyglm(I(sch.wide=="Yes")~ell+meals+mobility+stype, design=dclus2, family=quasibinomial())
anova(model2)
anova(model0,model2)
anova(model1, model2)
anova(model1, model2, method="Wald")
AIC(model0,model1, model2)
BIC(model0, model2,maximal=model2)
``` |