Maximizing Cronbach alpha to select the number of variables that define a given construct I can't seem to find this anywhere on the internet or in my books. I'm putting together a construct for an underlying variable.
Is it acceptable to have a construct with two variables if that produces a bigger Cronbach alpha than the construct with 3 variables in a professional statistical analysis?
Using 2 variables seems a bit on the low side, but it produces better results.
 A: The unstandardized Cronbach's alpha on two items does not make much sense, see e.g. The reliability of a two-item scale: Pearson, Cronbach, or Spearman-Brown? (International Journal of Public Health 58(4):637-642). You can also think in terms of of item correlation with the total score when correcting for overlap, see, e.g., W. Revelle's textbook on psychometrics (chapter 7). As for a good reference, I would recommend Test theory: A unified approach, by R.P. McDonald (1999), who suggested 3 items per dimension for uncorrelated factor models, IIRC, which is also handy when it comes to estimate the parameters of a CFA, and Psychometric Theory, by Nunally and Bernstein (1994).
Beware also that using a statistic like "alpha if item is deleted" without cross-validation is proned to over-fitting (the alpha is already a lower bound for reliability, but sample reliability may appear higher than population-level reliability when further capitalizing on chance), notwithstanding the fact that constuct coverage (or validity) may be quite poor when using only two items.
