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I have a dataset of project case studies for a new type of research method for Government agencies to support decision making activities. My task is to develop an estimation method based on past experience for future projects for estimation purposes.

My dataset is limited to 50 cases. I have 30+ (potential) predictors recorded and one response variable (i.e. hours taken to complete the project).

Not all predictors are significant, using step-wise selection techniques I'm expecting number of prediction variables is likely to be in the 5-10 variable range. Although I'm struggling to get a predictor set using the standard appraoches in tools like PASW (SPSS).

I'm well aware of all the material talking about rules of thumb for sample sizes and predictor variable to case ratios. My dilemma is that it's taken close to 10 years to collect 50 cases as it is, so it's about as good as it will get.

My question is what should I do to get the most out of this small sample set?

That is any good references for dealing with small smaple sets? Changes in p-value significance? Changes to step-wise selection approaches? Use of transforms such as centre-ing or log?

Any advice is appreciated.

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As you want to select a few predictors from your data set, I would suggest a simple linear regression with $L_1$ penalty or using the LASSO (penalized linear regression). Your case is suited for regression with LASSO penalty as your sample size, $n = 50$, and the number of predictors, $p=30$. Changing the tuning parameter will select the number of predictors you want to choose.

If you can give details about the distribution of your variables, I can be more specific.

I don't use SPSS, but this can be done easily in R using the glmnet function in the package of the same name. If you look in the manual, it contains a generic example (very first one, for gaussian case) which will solve your problem. I am sure, similar solution must exist in SPSS.

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  • $\begingroup$ The response is very much negatively skewed. With the majoirty of projects around 2500 hour mark and a tail stretching out to a couple of 10000-14000 hrs projects. The continous (scale) predictors are a mix of distributions while some predictors are categorical (nominal). What types of distributions are required for LASSO (or what else do you need to know from me)? -- btw thanks for the response! $\endgroup$ – Shane Feb 14 '11 at 6:21
  • $\begingroup$ @Shane, the LASSO is a general concept of penalizing with $||$ (modulus or absolute value) function. It is independent of any distribution. If you check the glmnet package (see function: glmnet), it gives you options to fit the glm (linear regression is a special case) with $L_1$ penalty for a variety of distributions. It is pretty fast and amazing at the same time. $\endgroup$ – suncoolsu Feb 14 '11 at 6:38
  • $\begingroup$ Checking SPSS help it talks about a feature called "Categorical Regression Regularization" or CATREG. It seems to address Lasso and Ridge methods. For some reason it's not enabled in my version. If anyone knows why I'd be appreciative. $\endgroup$ – Shane Feb 14 '11 at 6:39
  • $\begingroup$ @Shane If my memory doesn't fail me, I have seen @AndyW post fancy SPSS code. It (code) impresses me all the time! $\endgroup$ – suncoolsu Feb 14 '11 at 6:48
  • $\begingroup$ @Shane, it appears the CATREG command has been around for quite a few versions of SPSS, but you probably need some advanced regression module/licenses to use it. In the current edition you need the "premium" stat suite to get this functionality. I would just suggest checking out the R packages suncoolsu mentions (its free!). $\endgroup$ – Andy W Feb 14 '11 at 13:36

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