# What regression analysis should I perform on my data and why?

I am a law student researching which factors influence the CSR (corporate social responsibility, GSE_RAW) behavior of companies. As my studies didn't offer any statistics courses, I'm having trouble to understand what type of statistical analysis I should perform on my data. After describing the data, I hope some of you can tell me more about this.

Two groups of possible factors / variables influencing CSR have been identified: company-specific and country-specific.

First, company-specific variables are

• MKT_AVG_LN: the marketvalue of the company
• SIGN: the number of CSR treaties the company has signed
• INCID: the number of reported CSR incidents the company has been involved in

Second, each of the 4,000 companies in the dataset is headquartered in one of 35 countries. For each country, I have gathered some country-specific data, among others:

• LAW_FAM: the legal family the countries' legal system stems from (either French, English, Scandinavian, or German)
• LAW_SR: relative protection the countries' company law gives to shareholders (for instance, in case of company default)
• LAW_LE: the relative effectiveness of the countries' legal system (higher value means more effective, thus for instance less corrupted)
• COM_CLA: a measurement for the intensity of internal market competition
• GCI_505: mesurement for the quality of primary education
• GCI_701: measurement for the quality of secondary education
• HOF_PDI: power distance (higher value means more hierarchical society)
• HOF_LTO: country time orientation (higher means more long-term orientation)
• DEP_AVG: the countries' GDP per capita
• CON_AVG: the countries' average inflation over the 2008-2010 timeframe

In order to make an analysis on this data, I "raised" the country-level data to the company-level. For instance, if Belgium has a COM_CLA value of 23, then all Belgian companies in the dataset have their COM_CLA value set to 23. The variable LAW_FAM is split up into 4 dummy variables (LAW_FRA, LAW_SCA, LAW_ENG, LAW_GER), giving each company a 1 for one of these dummies.

This all results in a dataset like this:

COMPANY MKT_AVG_LN ... INCID ... LAW_FRA LAW_SCA ... LAW_SR LAW_LE COM_CLA ... etc
----------------------------------------------------------------------------------
1      1.54          55          0       1          34     65     53
2      1.44          16          0       1          34     65     53
3      0.11           2          0       1          34     65     53
4      0.38          12          1       0          18     40     27
5      1.98         114          1       0          18     40     27
.       .             .          .       .           .      .      .
.       .             .          .       .           .      .      .
4,000    0.87           9          0       1           5     14     18


Here, companies 1 to 3 are from the same country A, and 4 and 5 from country B.

My DV, GSE_RAW is a numerical value for each companies' CSR behavior given by a rating agency.

• I believe the country-level variables are also called "categorical" variables, as many companies share the same value for these variables (in the example above, companies 1 to 3 all share the same values for LAW_FRA to COM_CLA). I believe to have found out that "categorical" variables are also known as fixed factors. Is all this true?
• I believe an OLS regression analysis is not the proper model here because of the categorical (country-level) variables. It has been proposed to use "Generalized Linear Models" (GLS), using the country-level variables as (fixed?) "factors" and the company-level variables as "covariates". Is this correct? And as a subquestion: why exactly is OLS not appropriate because of the country-level variables? What is it what they do in the OLS calculations that makes them set off the regression?

[edit 1] I am using SPSS for statistical analysis

[edit 2] Here my attempt to create a GLM using this data. However, I am unable to not get the "you haven't specified a custom model" Do I have to select all 4 variables here (becaus I want a beta and significance level for all 4 of them to construct a regression model)? And if so, why do I have to do this twice? I already said in a previous dialogue box that DEP_AVG and CON_AVG are fixed factors and that SIGN and INCID are covariates. Why would I, for instance, insert INCID here as a covariate, but not include it in the model building dialogue? Also, I really don't understand the output I'm getting, since it is very different from ordinary OLS output (the only output I'm slightly comfortable with).

• Am I now doing the right analysis?
• How can I get a regression model from this?

• I thknk there's no point "raising" the country level data to the company level, because all companies from a specific country will share the same combination of country-specific variables. Mathematically, that means that $COUNTRY = a_1\cdot LAWFAM + ... + a_n\cdot CONAVG$ (where the $a$s are weighting scalars), and this term will be interchangeable in all models (the $a$s will be different for different models, but the same for each row of data for a given model). That means that raising your data is causing you to do more calculation, but not actually giving you any more information. – naught101 May 2 '13 at 0:25
• What does that mean? That I can perform 2 separate regressions (one for COUNTRY variables on 32 countries and one for COMPANY variables on 4,000 companies) and combine them into one model? So COUNTRY = a1 x LAW_FAM + ... + an x CON_AVG and COMPANY = b1 x MKT_AVG + ... + bn SIGN, combined into CSR = a1 x LAW_FAM + b1 x MKT_AVG + ... + an x CON_AVG + bn x SIGN? – Pr0no May 2 '13 at 7:56
• No, it means that the regression against $(MKT_AVG_LN, SIGN, INCID, COUNTRY)$ will give you the same overall results for each company relative to each other company as a regression against $(MKT_AVG_LN, SIGN, INCID, LAWFAM, ..., CONAVG)$. i.e. the strength of the effect of the first three (company-specific) variables will be the same in both of those models (because all of the country-specific variables are the same for every company in that country). – naught101 May 3 '13 at 3:43

Whether a variable is categorical depends only on the variable, not on any "sharing" of common values. In your case, LAW_FAM is categorical because it has four discrete categories: FRA, SCA, ENG, GER. In particular, LAW_FAM is nominal: the categories have no ordering. You could have several countries which happen to have exactly the same DEP_AVG, but that doesn't make DEP_AVG a categorical variable.

I would suggest that you look at Multilevel/Hierarchical Models, since you have hierarchical data: country-level data and company-level data nested within countries.

Your post is very good: you include enough details to help us help you. One more thing that would also help us point you in the right direction is to know what software you will be using for your analysis.

EDIT: You ask about Generalized Linear Models, which are chosen for specific kinds of dependent variables. For example, if you were wanting to predict a categorical variable, you'd use Logistic Regression (which is done with a GLM).

• Thanks, I've added SPSS to both the post and taglist. Don't I have "country-level data nested within companies" instead of "company-level data nested within countries" or am I misunderstanding you? Also, what I forgot to mention, is that the distribution of companies over countries is inequal. For instance, 40% of the companies in my dataset come from the USA, whereas only 3 of the 4,000 companies come from Taiwan. I don't know if this is essential information regarding the model I should use... – Pr0no Apr 25 '13 at 13:49
• I've read that Multilevel models are also known as mixed models, and SPSS has a Analyze > Mixed Models menu. I don't know where to go from there though because I have to choose between "Linear" and "Generalized Linear". What is the difference between them and which one do I need? To be clear: I need a regression output so that I can report a regression model like CSR = b1*MKT_AVG_LN + b2*SIGN - ... + b13*CON_AVG. – Pr0no Apr 25 '13 at 14:02
• What kind of variable is your CSR? Generalized Linear models are used for specific types of dependent variables, so my first thought would be "Linear". – Wayne Apr 25 '13 at 14:21
• The CSR variable (DV) is called CSR_RAW and it is a score starting at zero. It is the sum of hundreds of variables, so CSR(company1) = 40 + 10 + 50 + ... + 5 + 14. So it is a ratio scale variable. I hope this answers your question? – Pr0no Apr 25 '13 at 14:27
• Sounds like you want "Linear", not "Generalized Linear", then. (In terms of specifics, I've never used SPSS so can't help there, but there are definitely SPSS users around here.) – Wayne Apr 25 '13 at 14:47

Your situation is a bit complicated. We just need to take a step back.

In order for us to run this regression we need to know what your research question / hypothesis is?

You might not have to use the GLM, but could build a model from the linear regression and use the "test method" (which is not available in the drop menu of SPSS and only in syntax) described below in the sytnax.

Please run this syntax and let me know if the output is what you were looking for:

DATASET ACTIVATE DataSet1.
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI(95) R ANOVA COLLIN TOL CHANGE ZPP
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT GSE_RAW
/METHOD=ENTER DEP_AVG CON_AVG
/METHOD=TEST (LAW_FRA, LAW_SCA, LAW_ENG, LAW_GER)
/SCATTERPLOT=(*ZPRED ,*ZRESID)
/RESIDUALS HISTOGRAM(ZRESID) NORMPROB(ZRESID).

• Thanks for your reply :-) I think this is indeed what I am looking for, although I am unsure about whether I need GLM or not. The more I read about it, the more I doubt between using GLM or OLS. Please refer to the output here and tell me your thoughts on this issue based on the output. Your help is much appreciated. – Pr0no May 1 '13 at 20:45

OK, let me get this straight. In response to your older question here, you're trying to fit a more complicated mixed/multilevel/hierarchical model (yah for terminology). Not having any experience with SPSS, this is going to be more general, along with some guesses at what SPSS is looking for via the screenshots provided (one-eyed leading the blind and all that).

1. Analyze->Mixed Models->Linear is the correct choice here.

• A note on terminology - you mention GLM or GLS several times. This isn't what you're trying to fit. A GLM "Generalized Linear Model" is when your response variable is not normally distributed (for example, success or failure). GLS is something I'm unfamiliar with.
2. The warning message you're getting seems to be because you haven't specified any effects. You'll notice that the model result only returns a coefficient for the intercept. It looks like SPSS wants you to declare your variables in the first menu, then declare what they are under Fixed and Random. Now, for fixed vs random (warning: terminology differs):

• For our purposes (and apparently for SPSS'), a fixed effect is an independent variables you're inserting into your model and estimating a coefficient for. So MKT_AVG_LN, SIGN, etc. All those country-wide variables you carried down and the source of all your questions go here

You'll need to go into the Fixed menu and specify them.

• A random effect is what makes this tick and different from OLS. This is where the grouping/multilevel stuff comes into play. Rather than estimating a coefficient for these variables, a covariance structure is estimated which imposes further structure in your model, mediating the non-independence of your country-level variables being carried down to the firm-level. The structuring of these can get exceedingly complicated very quickly, but let's keep things simple here.

You will need a variable indicating the country (let's call it COUNTRY). This should be placed under Random->Subjects

3. Further notes:

• It would appear that factors = categorical variables and covariates = continuous variables here. I see you have DEP_AVG and CON_AVG under factors. These are (probably) not categorical variables, and should be moved.
• It looks like COUNTRY, LAW_FAM should be your only factors. Perhaps the other two LAW variables as well.

As I mentioned before, I don't use SPSS, so this is me eyeballing things and hoping things work out, while hopefully imparting some idea of how mixed models work.

• Thanks for your reply. It was indeed suggested by @gmacfarlane that I should break out the mixed question into a new post. DEP_AVG is actually the revenue of a countries' financial system relative to the countries' GDP. CON_AVG is the concentration of the banking system (marketshare of 10 largest banks relative to all banks), so if I understand correctly, they are in fact factors as well. I have to figure out how to get (the already existing) variable COUNTRY under random->subjects as this part of the dialogue box is greyed out default, but I'll manage. I'll post an update tomorrow! – Pr0no May 2 '13 at 21:01

I think that you are missing two critical factors. If you try to make a model of gravity but do not take into account mass or inter-mass distance, then no model will work well.

http://www.ted.com/talks/geoffrey_west_the_surprising_math_of_cities_and_corporations.html

I just love standing on the shoulders of giants. As much as I wish I were a giant, I always see farther with their help.

You need the company-specific variables that include "the current number of employees", "the cumulative sum of all employees over the life of the company", and "the age of the company".

I would also include the "cumulative revenue of the company" and "the current gross revenue".

Now I do not use SPSS. I do not speak its language. I do, however know a little about models. I would suggest use of a random forest to determine which of the variables in this collection inform GSR_Raw. Once you get an idea of which variables are worthless then you can remove them from your model, and simplify your analysis.

After you have a reduced model and are sure the inputs inform your output, then you can start trying to fit models. Start with the basics. Don't leap into crazy stuff until you are sure that the basic models don't do a "good enough" job.