My data consist of two sets. First set has 6 numerical variables (columns) and the second set has 16 numerical variables (columns). These two sets have ~150 rows.
Any suggestions?
My suggestion would be: rethink your question, set up some hypotheses about your data and after that ask what tools to use to check these.
Eik Vettorazzi, thank you for your answer. However, before setting up some hypotheses, I need to know the whole picture of "the relationship" among variables of the first and second set. Such as, which variables of the second set are highly contributing to the some variables of the first set?
To me it sounds like a case where partial least squares regression (PLS) might be well suited. PLS is a projection method that allows you to evaluate the relationship between a matrix of "explanatory" variabels with a matrix of "response" variabels. For the fundamental idea behing see this Wikipedia article here http://en.wikipedia.org/wiki/Partial_least_squares_regression - Hope this helps & Good luck!
Dear Turkay, when we have two sets of variables to find the relationship between them the best way is to consider them simultaneously. In other words if we want to find a relationship between, namely, one of your 6 variables and other 16, we should consider the relationship between these 16 and the 5 remaining variables.
I'm sure the best statistical analysis for such data is Canonical Correspondence Analysis (CCA) which consider all the variables simultaneously. you can perform this analysis using PC-Ord or PAST softwares simply.
Regards
Turkay,
I agree that either PLS or Canonical Correlation is a good choice for the question as framed, though I encourage you to strongly consider Elk's suggestion, even after your caveat.
PLS and CCA will probably give you very similar results in this situation, with the biggest difference being that the 1st PLS variates from each set will be maximally correlated. PLS focuses the variate weights on predictive utility to the other set, whereas CCA focuses them (if I recall correctly -- it's been a very long time, so I might not) on variance accounted for in their own set.
Read this for more info on PLS and CCA Difference:
http://www.diva-portal.org/smash/get/diva2:288565/FULLTEXT01.pdf
Ronny, That's a good point. I don't think Turkay has said whether his items would be expected to meet a common factor model (by set), but if they do, that's probably going to be a lot more straightforward and informative than what the rest of us have been talking about!
Dear Turkay,
If you don't have a clear hypothesis for the relationship between the two sets of variables, you can also use DATA MINING techniques. These models are very useful to find complex relationships between sets of variables. In some models, no statistical assumptions for the variables' distributions are needed. Artificial Neural Networks, or algorythms like C5, or for example, random forests, could help you to find a model.
All the best.
Canonical correspondence analysis will get you started in seeing what is going with you variables associations!
Thank you all for the constructive answers.
Recently, I have tried several methods on my data with my statistics software. Some data mining techniques appear to give results that are more relevant. However, results are sometimes hard to interpret. As always, statistics methods require steep learning curve.
I have tried using Multivariate Adaptive Regression Splines (MARSplines), Random Forests, Boosted Tree Regression and Regression Tree Models. In my case, these methods appear to be a good choice for analyzing and knowing predictors’ importance, and these methods appear to be handling one continuous dependent variable and several independent variables.
Finally, I decided to use Canonical Correlation Analysis (CCA), which I believe for my analysis, is a good choice for investigating the relationship between two sets of numerical variables. The CCA allowed several continuous dependent variables and several independent variables. At the end, I obtained these equations:
U1 = 0.37×F1_ES – 0.11×F2_ES + 0.07×F3_ES – 0.03×F4_ES + 0.11×F5_ES + 0.19×F6_ES – 0.11×F7_ES – 0.07×F8_ES – 0.46×F9_ES + 0.60×F10_ES – 0.17×F11_ES + 0.32×F12_ES + 0.10×F13_ES – 0.12×F14_ES + 0.13×F15_ES – 0.44×F16_ES
and
L1 = – 0.81×CUST + 0.16×INFR + 0.15×ITRN + 0.57×LOGS – 0.40×TIME + 0.97×TRAC
Canonical R = 0.93 and p
Do the sets of these numerical variables measure the same construct? If so you can create factor scores for them. Then you can use one of the statistical procedures of continuous outcomes
First of all you need to check the interrelationship among these variables after that you will be able to check the relation between the two type of variables....
This should depend on your research questions. If it's a "fishing expedition" you're bound to turn up significant correlations simply by chance. I think factor analysis or some similar data reduction techniques would be useful, but remember that these are based on correlation and covariance structures, and typically assume linear relatiosnhips. I would select some variables from each set and explore their bivariate relationships graphically before rushing to a multivariate analysis.
T- test can be used to find p-value which the results can be accepted if p-value is less than 0.01
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