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I carried out a linguistics experiment where I gave a text for people to comment on. I recorded and transcribed their comments. I would like use the number of utterances per sentence in the text they were given as a dependent variable in a linear model - would that be OK or would a poisson model be more appropriate in this case? A few additional details: (1) Subjects could spend as long as they wanted on the task, i.e. the number of utterances per sentence increases with time and there is no limit; (2) There are no zeros in the data as subjects were required to at least read the text they were given and reading itself is regarded as an utterance in the study; (3) The average number of utterances per sentence is around 5, with a few cases of up to 30 utterances, so I'd probably need to log-transform the data if I were to use a linear model.

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  • $\begingroup$ Is your response a count, then? $\endgroup$ Oct 9 '14 at 22:16
  • $\begingroup$ Yes it's a count. $\endgroup$ Oct 9 '14 at 22:18
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If you have a count, don't take logs, model the count (possibly with a log-link).

You might use a Poisson or quasi-Poisson model, but if you expect heterogeneity (other than that accounted for by your model), you may be better to use a negative binomial model, or perhaps even Conway-Maxwell-Poisson.

If you model the raw data using least squares, then (aside from any consideration that the mean may not be linear in predictors) there will very likely be heteroskedasticity (the variance will tend to get larger as the mean does), and you'll tend also to have some right skewness in the conditional distribution, but taking logs will overdo both, and tend to leave you with heteroskedasticity in the other direction, and left-skewness. Better to use a model that is more suited to the data at hand.

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