**Multi-way
Regression: A Closer Look at Water and Sanitation**

To run the complete analysis for modeling the effect of water and
sanitation on nutrition status, then a logical progression must be made by starting simple
with one variable (e.g., sanitation -**notoilet**, water source- **dpiped,
dwell**) and then adding variables into the model one by one. Use the
following exercises to run the regression models.

Model 1: Look at only toilet with the outcome WAZ score.

1. Open

keast4j.sav2. Click on

Statistics, Regression, Linear...3. Enter the

Dependentvariablewazfrom the variable list using the arrow key.4. Enter the

Independent(s)notoiletfrom the variable list using the arrow key.5. Select the model type as

Enterand click onOK.

**INTERPRETATION:**

The size of the effect of not having access to a safe toilet is large
enough to merit attention (B=-0.255), and it is significant (p=0.044). But this step
is just a first sighting and must not be taken as truth until further exploration is
pursued using other independent variables that we have discussed (e.g., water source,
education, roofing quality). Try the next step and see how the coefficient for **notoilet
**changes.

Model 2: Look at only piped water then only well water with the outcome WAZ score.

1. Open

keast4j.sav2. Click on

Statistics, Regression, Linear...3. Enter the

Dependentvariablewazfrom the variable list using the arrow key.4. Enter the

Independent(s)dpiped(... then run again with onlydwell) from the variable list using the arrow key.5. Select the model type as

Enterand click onOK.

*Piped water...*

*Well water...*

**INTERPRETATION:**

Only the model for piped water shows any significant influence in the model (B=0.369, p=0.007), whereas well water does not appear to have a sizeable or significant association with the outcome variable. We will now continue by running a model with no toilet and piped water to see how the coefficients are affected by the combination.

Model 3: Look at no toilet and piped water with the outcome WAZ score.

1. Open

keast4j.sav2. Click on

Statistics, Regression, Linear...3. Enter the

Dependentvariablewazfrom the variable list using the arrow key.4. Enter the

Independent(s)notoiletanddpipedfrom the variable list using the arrow key.5. Select the model type as

Enterand click onOK.

**INTERPRETATION:**

Now you can see the change in the coefficients from the previous models. The size of the coefficient for toilet has decreased slightly from -0.255 to -0.209 and is no longer significant in the model (p=0.101) at the 0.05 level. The variable for piped water still has a large coefficient, although it has decreased slightly as well from 0.369 to 0.335. Piped water still seems to be significant in the model to test possible causal factors for malnutrition. So, what are we not looking at yet that might still be influencing the model? The question we asked was what is the effect of water and sanitation above and beyond the influences of education, therefore we should try adding education in the model and then see how the coefficients behave. We have previously looked at education alone and found it has a strong association with waz score, therefore we will skip on to a full model with toilet, water, and education together.

Model 4: Look at no toilet and piped water with the outcome WAZ score.

1. Open

keast4j.sav2. Click on

Statistics, Regression, Linear...3. Enter the

Dependentvariablewazfrom the variable list using the arrow key.4. Enter the

Independent(s)notoilet,dpiped,anddlowednfrom the variable list using the arrow key.5. Select the model type as

Enterand click onOK.

**INTERPRETATION:**

Now you can see the change in the coefficients for water and sanitation.
It is clear that there is uncertainty as to whether or not either of these have an
influence in nutrition status any longer. Our worry is that they actually do, but we
are not detecting it due to the strong collinearity with education. We would be more
certain about the results if the effect was independent of education, but since we have
previously detected collinearity, it might be best to now look deeper by looking within
education groups to see what the behavior is for toilet and water source. You have
done this in previous exercises using the routine called *Select if...*, which is
quite simple. Here is how to select for the low education group and then how to run
the model again.

Model 5: First select for dlowedn=1 (the low education group) and then run a model for notoilet and piped water.

1. Open

keast4j.sav2. Click on

Data, Select Cases...and then click on the dot forIf condition is satisfiedand click the box forIf...3. Move the variable

dlowedninto the white box using the arrow key and type in=1, so that the box readsdlowedn=1.4. Click on

Continueand then make sure the dot byUnselected Cases areis onFILTERED(very important!!!!).5. Click on

OK.

Now that your cases are selected for low education group (<primary).1. Open

keast4j.sav2. Click on

Statistics, Regression, Linear...3. Enter the

Dependentvariablewazfrom the variable list using the arrow key.4. Enter the

Independent(s)dpipedfrom the variable list using the arrow key.5. Select the model type as

Enterand click onOK.

**INTERPRETATION:**

Now the result with only the low education group is run for only piped water. If you were to check with no toilet in the model as well, you would have found the same problem of interaction between the variables and no effect from either. When looking at piped water and waz score for only the low education, there is a still not a significant coefficient and it is quite small anyhow. There might be no effect of water source for those that are not educated. It could make sense to have a result like this since those who do not have a basic level of education might not know how to properly use a better water source. Lets look further to see if there is a different result for the group that does not have low education.

Model 6: First select for dlowedn=0 (not low education group) and then run a model for notoilet and piped water.

1. Open

keast4j.sav2. Click on

Data, Select Cases...and then click on the dot forIf condition is satisfiedand click the box forIf...3. Move the variable

dlowedninto the white box using the arrow key and type in=0, so that the box readsdlowedn=0.4. Click on

Continueand then make sure the dot byUnselected Cases areis onFILTERED(very important!!!!).5. Click on

OK.

Now that your cases are selected for better education group (<primary).1. Open

keast4j.sav2. Click on

Statistics, Regression, Linear...3. Enter the

Dependentvariablewazfrom the variable list using the arrow key.4. Enter the

Independent(s)dpipedfrom the variable list using the arrow key.5. Select the model type as

Enterand click onOK.

**INTERPRETATION:**

Here is the result for those that do not have low education (**dlowedn
=0**), which is clearly different from the same model run for those that do
have low education. The variable for piped water now has a coefficient far larger
(0.353 compared with 0.096) than in the previous model. This fits with the idea that those
with better education would be more affected by improved water because they might be more
inclined to use it properly. But what if this is just another red herring and it is
actually just a difference in socio-economic status in this higher education group that is
causing this result to appear. It might be a good time to test the model by adding a
variable to control for socio-economic status such as roofing quality (**dbadro**)
to control for this. Try it now.

Model 7: First select for dlowedn=0 (not low education group) and then run a model for piped water and roofing quality.

1. Open

keast4j.sav2. Click on

Statistics, Regression, Linear...3. Enter the

Dependentvariablewazfrom the variable list using the arrow key.4. Enter the

Independent(s)dpipedanddbadrofrom the variable list using the arrow key.5. Select the model type as

Enterand click onOK.

**INTERPRETATION:**

Well, this model did change the coefficient for piped water, but not drastically and the size of the coefficient is still large with a significant p-value (B=0.344, p=0.042). I would believe that this would be support for causality when looking at the effect of water source on nutrition status. This would likely be an effect seen only in those with a basic level of education (>primary).

BE SURE TO GO BACK THROUGH THE SELECT IF ROUTINE and !!!!