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Appropriate regression or alternative for small sample

Posted: Sat Jan 27, 2018 10:16 am
by Mait
In my research model there are seven independent and four dependent variables, each measured by multi-item perceptional Likert scale either from 1 to 5 or from 1 to 7 (no categorical variables). Scale length variety is due to using various pre-validated questionnaires. The plan is to test independent variables' impact on each dependent variable by multiple regression.

Unfortunately final dataset contained 26 respondents measured at one point of time (“cross-sectional”) from company of over 2’000 employees, making representative sample to be around 330. Parametrical tests are not applicable in case of small sample (n=26), but finding appropriate non-parametric test turned out to be surprisingly difficult. I came crossed with several different, partly contradicting opinions from internet, not clearly applicable by SPSS. Some recommend simple regression that is basically the correlation, other continue the line by recommending the Kendall correlation for small samples. Third ones recommend Lasso and Elastic Net for situations where there are more variables than responses (pretty close here – 11 multi-item variables and 26 responses), valid for numeric and categorical dependent variable (here numeric). Forth ones recommend Cox regression, but this is for time series/longitudinal (here cross-sectional). Fifth ones suggest to pick single explanatory variable by principal component analysis and run simple regression (phenomenologically hard as independent variables belong to two very different groups – one individual level, second group level, and idea is not to operationalise measures differently, but bring out the impact on dependent variables). Sixth ones recommend Direct Eigenvalue Estimator (DEE) for small sample regression, but there was not much information about it for SPSS. Seventh ones mention CNLR procedure. There were more recommendations (SEM etc.) available.

I am using SPSS 22, what regression if any would you recommend for small samples?

Re: Appropriate regression or alternative for small sample

Posted: Sat Jan 27, 2018 12:49 pm
by statman
Very limited so need to look for alternatives, e.g., independence test

Also..................

Re: Appropriate regression or alternative for small sample

Posted: Sat Jan 27, 2018 4:54 pm
by Mait
I am using SPSS 22 (Windows XP) for managerial research where five individual level personal traits and two group-level organizational culture variables construct independent variables, dependent variables are four group-level organizational learning process components. Apologies if missed anything!

Further details for independence test would be useful! I have calculated some non-parametric tests, such as Spearman linear rank correlation coefficients and Kendall tau non-linear rank correlation coefficients – is this the so called simple regression!? On the other hand, independence test is also one of the assumptions for multiple regression, even the values were observed to be independent, should the Durbin-Watson test of independence of errors to be performed as well? What does it give us if the aim is not to perform multiple regression?