I am trying to build a regression model where I have 25 independent variables(predictors) all of which 5 point Likert items and 1 dependent variable which is a mean score of a 7 point Likert scale (aggregated score). I need to filter the best possible predictors(variable selection) from these 25. I was wondering what type of regression should I use, linear or ordinal ?
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$\begingroup$ I edited my question so hopefully it is clearer now. I read that Likert items are considered ordinal but Likert scale aggregated scores can be considered interval and thus analysed parametrically. Since my DV is a mean score can I use multiple linear regression? $\endgroup$– DanaiMar 12, 2017 at 14:37
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$\begingroup$ I agree that multiple regression is a good choice. However, I think your source is confusing ordinal/interval with discrete/continuous. $\endgroup$– David LaneMar 12, 2017 at 14:56
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$\begingroup$ So I have two questionnaires, one is assessing the usability and one is assessing the agents' persona in an application. The usability questionnaire is a 7 point Likert scale from strongly disagree to strongly agree that consist from 18 Likert items. My DV is the Usability mean score of all 18 items. The other questionnaire (agents' persona) is a 5 point Likert (strongly disagree-strongly agree) scale with 25 Likert items that I want to use as predictors. Both questionnaires are validated classic Likert. I have gathered my data already. $\endgroup$– DanaiMar 12, 2017 at 17:10
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$\begingroup$ I am using SPSS to analyse my data and I have transformed them to numeric values 1-7 and 1-5 if that helps. $\endgroup$– DanaiMar 12, 2017 at 17:13
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1$\begingroup$ From my pov there is no single correct answer to your question. Given that, I would regard prescriptive comments as suspect. It sounds like the context of your analysis is a marketing one in terms of trying to understand the "drivers" of an average usability score. I think you need to provide more info, e.g., are these averages over a fixed window of time, e.g., a minute, an hour, a day, etc.? Are there multiple periods of time? What's the total amount of time gathered? How are the two surveys linked? And so on. $\endgroup$– Mike HunterMar 13, 2017 at 14:39
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I think I get it, too many questions. However, obtaining answers to them is important for a good recommendation.
One approach to answering your regression question would be to use the Lasso, a regularizing method, for variable selection. That said, every statistician and their sibling has a "favorite" variable selection method. The Lasso has the advantage of being called out by Larry Wasserman on his defunct Normal Deviate blog as one of the 10 best contributions to statistics in the last 10 or 20 years. The Lasso would reduce 25 variables down to a more manageable fewer number.
Then, there are plenty of heuristics for ranking variables by their relative importance, i.e., identifying the "drivers." A bad choice to avoid is using the betas or regression coefficients since they are not scale invariant. A better choice would be to rank the absolute values of the t-statistics associated with each variable. An "optimal" choice to relative variable importance would be to read Ulrike Groemping's papers on this area of statistical modeling and implement her own approach called RELAIMPO... https://prof.beuth-hochschule.de/groemping/relaimpo/.
answered Mar 13, 2017 at 22:19
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$\begingroup$ @StudentT That's a little cryptic. Would you elaborate so the OP can obtain the full intentions of your insight? $\endgroup$ Mar 14, 2017 at 2:31
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1$\begingroup$ @StudentT is correct in noting that stdzd betas are a conventional practice in determining relative variable importance. This is not without controversy. For instance, an American Statistician paper (sorry, no longer have the reference) took issue with this approach, suggesting that it was not appropriate since the standardizing occurs prior to the estimation of the coefficients and, therefore, was an unconditional process. Of course, the coefficients produced are conditional on the presence of the other variables in the model. One way to avoid this is simply to use other heuristics. $\endgroup$ Mar 14, 2017 at 17:05
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