Chi-Square-Automatic-Interaction-Detection (CHAID) is a predictive modeling method available on a variety of analytical platforms (SPSS, SAS, R, etc.). For initial exploration of a multivariate data set where the goal is to identify the statistically significant (at any standard confidence level p < 0.1, 0.05, 0.01) candidate variables (either Dependent or Independent) and their interactions in a hierarchy, CHAID modeling would be my first choice. If a candidate Dependent Variable (i.e. Return On Assets) is a scale level of measure, consider dichotomizing into a binary categorical level of measure (Yes/No). Binary CHAID models produce a model probability statistic (like the C Statistic in Binary Logistic Regression models) that can be used to evaluate model sensitivity vs specificity (Area Under the Receiver Operating Characteristic Curve) AUROC Curve. Trim the CHAID model by pruning the resulting hierarchical tree by removing variables from the model that do not have any significant interactions in the hierarchical tree (at the specified alpha error level used to build the model). Once you have a trimmed model with an AUROC Curve that has an area of 0.75 or more (i.e. 0.75 and above is a Good model in the heuristics of AUROC) then use that list of variables in the CHAID model, in a Binary Logistic Regression (BLR) model. The BLR model will provide Odds Ratio's (Exponents) for each of the Independent Variables (predictive factors) in the BLR model. Trim this BLR model to remove any insignificant (p < specified experiment-wise alpha for for model), and then evaluate the resulting AUROC Curve for the final trimmed model. Internal cross-validation can be done by putting this final set of Independent Predictor Variables into a CHAID model, and comparing the two AUROC model probability curves (one from BLR, the other from CHAID). They will closely agree, and the ordered hierarchy seen in the top down tree branching shown in the CHAID model will generally match the hierarchy among the Odds Ratios (OR) seen in the BLR model.

The real test of the models is external replication by a third party using a similar, but totally different data set. You question about time series? If you have the luxury of a calendar date for each row of data in your model, then convert the date into dichotomized (dummy coded Yes/No) Week-Year variables, Month-Year variables, Quarter-Year, or Year independent predictor variables. Retain all significant variables, trim all insignificant variables in the model. The final trimmed models will show what (if any) time periods (week, month, quarter, or year) were statistically significant predictors (or not by their absences) of the Target Dependent Variable being predictively modeled. The two methods (CHAID and BLR) will demonstrate the odds of the probability of Return on Assets (at the selected level of dichotomy (50%, 75%, 90%, ... ) and their hierarchy of interaction.

Finally, when a predictive model achieves a good (or better) AUROC and the model contains only significant variables in the model, then and only then can those independent variables be described as being "independently predictive". This is the ultimate goal of BLR, as it then becomes possible to combine predictive factors by multiplying their Odds Ratios (as they are exponents of the beta weight in the model). If the OR of factor A is 2.5 and the OR of factor B is 3.0 then the combined probability of the DV = Yes (1) when considering A and B being both being Yes (1) is 2.5 X 3 = Odds Ratio of 7.5 (Seven and a half times more likely, 750% more likely that the DV will be Yes rather than No. What of factor C with OR of 1.5 is also true? Then 2.5 X 3 X 1.5 = 11.25, the DV has a 1,125% probability of being Yes rather than No, in this final trimmed model.

Your mileage may vary, but this is how I would initially approach this type of data mining question towards building a standard model to use on this type of data.

As self-confessed non-statistical gurus :-), let me provide non-technical guidance. The type of data that you have is called panel data. Panel data are those data that consist of cross sectional observations (records/data on 75 companies in your case) over a times series (5 years). SUR (or 3 Stage Least Squares if you have endogenous right hand-side variable) is only valid for cross sectional data. To apply SUR you will have to estimate more than one equation jointly. For argument sake, let us assume you were planning to estimate two equations: one to explain return on asset and the other to explain return on equity for these 75 companies. SUR will be a more efficient estimator to use, rather than estimating these equations one at a time. But from my understanding, that is not the case with your work. You are interested in using these multi-year data set to estimate one equation, right? If so, you can't use SUR.

Depending on the properties of your independent variables, you may be able to use simple regression or other forms to estimate your equation using data for one year at a time. However, that will be grossly inefficient as you already have a rich data set that gives you more information.

What you need to do is to use a panel data estimator. I suggest you read up on Fixed Effect and Random Effect models, which are two popular models for panel data. Depending on the structure of your data, one will be more appropriate than the other. However, since you're not a Statistician or Econometrician, I may end us confusing you the more if I try to explain the difference. Suffice to say, check out any good econometrics test book on panel data estimation.

Hope you find this useful.

Abdullahi Abdulkadri Thank you for a good answer.

Yes, we would like to test for Return on assets and Tobins Q as dependent variables, and we have a number of different observations as independent variables for 75 different companies collected over a 5 year period. In our case, we are going to test for "inside share holding" and if it has any significance on the ROA and Tobins Q. Does this mean that SUR might be an approach anyway?

Best Regards,

Simon

Simon Olsson The additional information you provided is very useful in understanding your study. In this case you have two options:

1. Use SUR to estimate the two equations (with ROA and Tobin's Q as your dependent variables) but you will need to estimate them with data for each year separately, giving you five sets of coefficients, each year having its own parameter estimates. You will be able to jointly examine the significance of inside share holding or its relative importance on ROA and Tobin's Q for each year using this approach. However, you will not be able to test, within the model, if these effects vary across time.

2. Use panel data estimation with data for 5 years to estimate each equation. Here you can test if the effect of inside share holding on ROA or Tobin's Q changes over time or not but you will not be able to compare the effect of inside share holding on the two measures since you're estimating the equations separately.

So, based on the outcome that is more important to your study, you can choose between the two options. You can also use both options and report/compare the results.

Check https://journals.sagepub.com/doi/full/10.1177/2633105520963045