Raftery (1986) [304]
Comment to Grusky and Hauser (1984)
[170]. Properties of LR test when $n$
is large. BIC proposed instead, favours quasi-symmetry model for the
data of [170].
Hout and Raftery (1988) [192]
(A CASMIN conference paper). BIC to address the large-$N$
problem. Example (from [Hauser (1984)]): $N=14 258$ French and
English men, class of origin, destination, country; homogenous
quasi-symmetry model selected. Other model selection problems discussed:
sparse tables and zero counts; nonnested models (e.g. continuous scales
vs. nominal levels) and combining them; mathematical vs. verbal
formulation of models and hypotheses.
Davis (1990) [105]
Survey of sample sizes in leading sociological journals. Role of
$N$ in significance testing. Discussion of (and formulas for)
$CN$, the sample size for which the observed effect would be
exactly significant at a given level.
Raftery (1995) [307]
Bayesian model selection for sociological audience. Problems with
standard hypothesis tests: $p$-values with large $n$ and
in multiple comparisons; selection from many (possibly nonnested)
competing models; model uncertainty. Bayesian approach to these;
derivation of BIC, examples of specific types of models, choice of
`$n$', interpretation and relation to p-values. Data of
Grusky and Hauer (1984)
[170] used as example of model selection in very large
data sets. Bayesian model averaging. Discussion in
[156] and [182], rejoinder in
[308].
Gelman and Rubin (1995) [156] Discussion of Raftery (1995) [307]. Mostly critical: argues that BIC attempts to provide rationale for selecting a model which does not fit. In his rejoinder, Raftery [308] comments that this is based on use of LR tests to decide which model `fits' and misunderstanding of the prior implied by BIC. G & S argue for the distinction between statistical and practical significance, i.e. whether a model is acceptable depends also on the intended purposes to which it is to be used. In general, G & S de-emphasise model selection, preferring complex models (embedding the main choices in a flexible class of models), collection of further data (to make selection easier) and, sometimes, model averaging.
Hauser (1995) [182]
Discussion of Raftery (1995) [307]. Very positive. Discussion
of large-$n$ model selection problems in Grusky and Hauser (1984)
[170] and the BIC resolution of them in Raftery (1986)
[304]. Further examples of the use of BIC in sociological
modelling. Recommendations for universal acceptance of BIC.
Weakliem (1998) []
Criticism of BIC for sociological audience. Main points: (i) BIC implies
(best approximates) a BF with a certain prior, which may or may not be
sensible; (ii) the `sample size' $n$ in BIC is not well defined,
should be amount of information in the sample but this is not easy to
define. Many other comments and suggested modifications to BIC.