Multi-way Regression

Details for the Analysis

Running a regression analysis is quite simple using SPSS.  The following steps will be used over and over to run seven different models.  The only changes you will make will be the independent variables that you insert for each run.  You are aiming to test each combination of variables to see how the coefficient changes for each variable as new variables are added to the model.  A good determinant of the outcome will remain significant in a model with a substantially large coefficient.  Keep an eye on the coefficients as you run each of these seven models.  This information will be summarized in the table of the main text.  This provides the nuts and bolts of how to get to that point.

Exercise in running regression analyses:

1.  Open keast4j.sav

2.  Click on Statistics, Regression, Linear and a table will appear for inserting the regression variables.

3.  Select the variable waz from the variable list on the left and insert it into the Dependent Variable box using the arrow.

4.  Select the variable dlowedn (this will change from model to model) from the list place it in the Independent Variable box using the arrow key.

5.  Click to choose the Method called ENTER.

6.  Click on OK

Take a look at model 1: considering low education as the independent variable and WAZ as the Dependent variable:

INTERPRETATION:

Take a look at the B coefficient associated with low education, as well as the t value and significance.  Low education does have a negative association (B= -0.448) with nutritional status at a significant level (p=0.000). The sample size is quite large (n=698) and the coefficient of determination R2 is 0.032 or in other words, 3.2% of the variability in the outcome is attributable to education.

Now, lets not jump the gun with interpretation.  Our goal is to look at many variables together in one model, but we are progressing one variable at a time to see the changes in the coefficients.  Try looking at bad roof quality alone and no toilet alone, then we will look at the combinations.  Use the same steps as shown above, just enter dbadro for the independent variable in the next regression, and then for the third run add notoilet alone.  Here are the results.

Take a look at model 2:  considering roofing quality as an independent variable and waz as the outcome variable:

Note that roofing is also significant, so that those with worse roofing quality are likely to have lower nutritional status.  The coefficient of determination is very small for this model.

For sanitation as an independent variable and waz as the outcome variable:

Again, you see that no toilet is associated with nutritionally worse-off children and it is significant (p=0.044) when alone in the model.  But this model does not control for any other factors that influence nutritional status.

Now take a look at model 3: considering education and roofing as independent variables in the same model with the outcome waz score:

As you see here, the size of the coefficient for low education has dropped slightly when you consider roofing quality in the model (from -0.448 to -0.420).  This is true for the size of the roofing coefficient as well (-0.253 to -0.158).  The coefficient of determination for this model is slightly higher now that two variables are being considered, than the models alone, but only very slightly.  The main interest here is that education is still significant in the model after roofing is considered, although roofing is not longer significant.

Take a look at model 4, including education, roofing and toilet as independent variables:

The coefficient for education has dropped again, but only slightly and it hangs on to the highly significant status (p=0.000).  It appears that both roofing and toilet are not as strongly associated with nutritional status, but they do play a role in determining the health of a child.  Now try looking at the variables for water source in a model and add them on to these three to see what the changes are.

First, look at piped water and well water in a model with the outcome variable waz score:

Now you see that piped and well water together as dummy variables make a small contribution to the model (r squared =0.008) and the coefficient for piped water is significant.

But now look at a model 5 with these variables and education and roofing.

Because your interest in this model is the effect of education, the findings are good so far.  There is still a significant and meaningful size of change in nutritional status associated with education, even when all of these other potential influencing factors are included. One remaining independent variable that could actually diminish the seeming effect of education status is the economic status of the family.  Try looking at a model that considers an income variable to see what the change is in education status.  But first look at income in a model alone.

Model 6 shows income by itself in a regression model with the outcome WAZ score.

As the results show, income like education is a significant and large factor in the model with nutritional status as the outcome.  The coefficient is very large (B=0.449) and in the expected direction, so that those with greater income have a greater likelihood of being better-off nutritionally.  Try a model now considering all of the variables with income included.

Model 7 has all variables included:

If you were worried about interaction between income and education, just run a quick Transform, Compute routine to create an interaction variable called vinc_edn by multiplying the two together.  When you run a model with education, income, and the interaction of the two, then the interaction variable is clearly not significant (p=0.9).   Therefore, this would be dropped and your model would default back to model 7.   Return to main text to see the interpretation of this model.