Bivariate analysis as a basis for a subsequent analysis? I have run across many research articles which used bivariate analysis, whose results become the basis for a subsequent analysis. For example, a Chi-squared test was used as a preliminary analysis to determine the factors that are significantly associated with a another nominal variable. That is, a series of Chi-squared tests was done. Subsequently, another analysis - loglinear analysis - was used; but, it only included factors that were found to be significantly associated during a series of Chi-squared tests. What are the pros and cons in this kind of statistical practice? If any, under what conditions/assumptions would this kind of practice be considered as reasonable?
 A: You seem to be talking about a series of bivariate analyses, as a way to select variables for a multivariable regression analysis (since you mention log-linear analysis)
I can't think of any situation in observational studies where this would be a good idea, particularly if the purpose of the model is inference, rather than prediction.
The main problem I see with doing this, is that the bivariate analyses may be considerably biased due to confounding or selection bias. Thus, conducting variable selection in this manner could very likely result in a multivariable regression model which then includes mediating variables (ie. variables which lie on the causal pathway between an exposure and an outcome). Including mediators in a regression model can invoke bias in the causal interpretation due to a phenomenon known as the reversal paradox - examples of which include Simpson's Paradox, Lord's Paradox and Suppression - See Tu, Y.K., Gunnell, D. and Gilthorpe, M.S., (2008) for further details.
A much better approach is to conduct a principled variable selection procedure, such as causal diagram or Directed Acyclic Graph (DAG), informed by expert knowledge of the domain. A DAG can be used to identify the minimum set of covariates that should be included in the regression model. An excellent and free online tool for doing this is Daggity (available at http://www.dagitty.net/) - see Textor et al (2016) for details of it's usage
References:
Textor, J., van der Zander, B., Gilthorpe, M.S., Liśkiewicz, M. and Ellison, G.T., 2016. Robust causal inference using directed acyclic graphs: the R package ‘dagitty’. International journal of epidemiology, 45(6), pp.1887-1894.
Tu, Y.K., Gunnell, D. and Gilthorpe, M.S., 2008. Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon–the reversal paradox. Emerging themes in epidemiology, 5(1), p.2.
