![Regression Diagnostics and Model Evaluation
Regression Diagnostics and Model Evaluation
Program Transcript
[MUSIC PLAYING]
MATT JONES: We've gone over estimating bivariate and
multiple regression
models, but one thing we haven't talked about up to this point
are some of the
assumptions of multiple regression models. It's very important
to adhere to these
assumptions to have proper interpretation of our models. These
assumptions](https://image.slidesharecdn.com/estimatingmodelsusingdummyvariablesyouhavehadplentyofop-221031044208-db6f7d65/85/Estimating-Models-Using-Dummy-VariablesYou-have-had-plenty-of-op-docx-2-320.jpg)
![I would
encourage you to look at other resources and to view this video
again. Lastly,
don't forget to reach out to your instructor if you have
questions.
[MUSIC PLAYING]
©2016 Laureate Education, Inc. 3
Dummy Variables](https://image.slidesharecdn.com/estimatingmodelsusingdummyvariablesyouhavehadplentyofop-221031044208-db6f7d65/85/Estimating-Models-Using-Dummy-VariablesYou-have-had-plenty-of-op-docx-8-320.jpg)
Estimating Models Using Dummy VariablesYou have had plenty of op.docx
- 1. Estimating Models Using Dummy Variables You have had plenty of opportunity to interpret coefficients for metric variables in regression models. Using and interpreting categorical variables takes just a little bit of extra practice. In this Discussion, you will have the opportunity to practice how to recode categorical variables so they can be used in a regression model and how to properly interpret the coefficients. Additionally, you will gain some practice in running diagnostics and identifying any potential problems with the model. To prepare for this Discussion: Review Warner’s Chapter 12 and Chapter 2 of the Wagner course text and the media program found in this week’s Learning Resources and consider the use of dummy variables. Create a research question using the General Social Survey dataset that can be answered by multiple regression. Using the SPSS software, choose a categorical variable to dummy code as one of your predictor variables. Estimate a multiple regression model that answers your research question. Post your response to the following: What is your research question? Interpret the coefficients for the model, specifically commenting on the dummy variable. Run diagnostics for the regression model. Does the model meet all of the assumptions? Be sure and comment on what assumptions were not met and the possible implications. Is there any possible remedy for one the assumption violations? Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.
- 2. Regression Diagnostics and Model Evaluation Regression Diagnostics and Model Evaluation Program Transcript [MUSIC PLAYING] MATT JONES: We've gone over estimating bivariate and multiple regression models, but one thing we haven't talked about up to this point are some of the assumptions of multiple regression models. It's very important to adhere to these assumptions to have proper interpretation of our models. These assumptions
- 3. include linearity, independence of error, homoscedasticity, multicollinearity, undue influence, and normal distribution of errors. Let's go back to SPSS to see how we can test these assumptions and evaluate our models. Let's go ahead and estimate a multiple regression model using respondent's socioeconomic status index is the dependent variable, respondent's highest education as an independent variable, and occupational prestige score as an independent variable. But this time, let's request some additional information to perform some diagnostics around our model. Go to analyze, regression, and linear, since we are still using an ordinary least squares method. We'll scroll down and enter my dependent variable first, respondent socioeconomic index. My independent variables of occupational prestige and highest year of school completed. I want to go over to statistics and request some additional information. I will request collinearity diagnostics, and Durbin-Watson of the residuals. Click continue. And we'll also click on plots and request a plot, my predicted against my residuals. I enter those and click continue. Lastly, I want to click on Save and request Cook's-- this is also called Cook's distance-- and my standardized residuals. Click continue. And once I click OK, the model will be
- 4. estimated, along with some tests for diagnostics. Looking at my first piece of output, the model summary, I want to pay attention to the Durbin-Watson statistic. The Durbin-Watson statistic has values from zero to 4.0. The Durbin-Watson statistic provides us with some information about independence of errors. A value of 2.0 for Durbin-Watson indicates there's absolutely no correlation between the residuals. As a very general rule, the values below 1.0 and values above 3.0 are considered quite dangerous and one might expect that the model suffers from rather serious serial correlation. Moving down to the ANOVA, we see that our overall model is significant. We have our coefficients output where we can interpret our individual predictors, but as part of our diagnostics, we want to pay attention to VIF. This is the variance inflation factor. ©2016 Laureate Education, Inc. 1
- 5. Regression Diagnostics and Model Evaluation As a general rule, values close to 10 and definitely above 10 indicate serious multicollinearity in the model. That means the independent variables have a high level of correlation between each other. We see here that the value of 1.4, for both of our predictor variables, are well below that 10.0 general rule. Therefore, we can assume that we've met the assumption. We requested a Cook's distance, which tells us something about undue influence that is specific outliers one or the variables that might be causing undue influence on the model. They might have a significant impact. We can go to our Cook's distance and look at the descriptives on our residual statistics. Again, as a general rule, Cook's distance values of 1.0 or greater are considered problematic and further diagnostics should be performed to
- 6. evaluate for possible undue influence on the model. We see here that our Cook's distance values range from a minimum of 0.0 to 0.025, well below the general rule of 1.0. We can assume that we have no undue influence in this model. After examining the Cook's distance, we can examine a histogram of the distribution of our errors. The assumption on multiple regression is the normal distribution of errors. As you can see from our histogram, our distribution is fairly normal. Therefore, we can conclude that we have met this assumption. Or, at the least, we do not have a significant deviation from normality. I should note that many modern statisticians see this assumption as of little importance to estimating regression models as it has little impact on the model. Next, let's look at the scatter plot which provides us with information about homoscedasticity, or whether our residuals at each level the predictor are equal in variance. As we can see here, there is no discernible pattern with the spread of scatter. If our model suffered from heteroscedasticity, we would see a grouping of scatter at one end that funnels out into a discernible pattern, often looking like a trumpet. If we double click our scatterplot, we obtain the chart editor. And I'm just going to
- 7. go add a fit line to provide a reference line. Once I add this reference line, you can see that there's no discernible pattern to the scatter. There are a couple of areas in the middle where I notice that the scatter funnels out slightly but it certainly doesn't look like a funnel or a cone shaped pattern. Scatterplot also provides us with some information about linearity as well. Remember that an assumption of regression is that the variables have some linear relationship to each other. Scatter, again, tells me that there is this linear relationship. If there was not a linear relationship, I might see a nonlinear relationship, in which the scatter perform a u shaped pattern. Regression diagnostics is a difficult topic, especially once you start to understand all the different ways in which your model can go wrong. There are entire ©2016 Laureate Education, Inc. 2 Regression Diagnostics and Model Evaluation textbooks written, and classes on regression diagnostics, and so
- 8. I would encourage you to look at other resources and to view this video again. Lastly, don't forget to reach out to your instructor if you have questions. [MUSIC PLAYING] ©2016 Laureate Education, Inc. 3 Dummy Variables
- 9. Dummy Variables Program Transcript DR. MATT JONES: Hi everybody, this is Dr. Matt Jones from the Center for Research Quality here to talk to you today about constructing dummy variables in SPSS. The purpose behind our conversation today is to show you how to construct these dummy variables to use as independent variables when you are fitting a multiple regression model or constructing a multiple regression model, And I have in front of us the Afro barometer data set. I've greatly simplified it for the purpose of this demonstration. You'll see, there are obviously only three variables in it, country in alphabetical order, country by region, and trust in government index. Now I might want to construct a variable or use a variable, country by region, that that might be relevant to my research question or might be an important controlling variable that I need to use in my multiple regression analysis. And it's very tempting just to throw it in as an independent variable as it is here. SPSS will allow me to do that. It will produce some output for that variable or coefficient so forth and associated p values. But the statistics generated really won't necessarily make any sense unless I'm creating a dummy
- 10. variable or set of dummy variables from this original variable. So if I go and click on values here, you'll see that there are five 4 attributes or four groups to this variable country by region, West Africa, East Africa, Southern Africa, and North Africa. And the rule is for creating dummy variables is the number of groups minus 1. That is there four groups here, four attributes to this variable. So I need to take 4 minus 1, obviously equals 3. I need to create three dummy variables. One variable is always left out if you will to service that reference category. And just again for the sake of simplicity, I'm going to leave number four, North Africa, as our reference category today. What you pick as your reference category might be dependent upon your research question, some theory, what it is you're trying to find out, again, very context specific. But, again, for today, just going to sort of randomly choose North Africa as our reference category. Before you create your dummy variable, you do want to note the original coding on the original variable here one, two, three, and four and what those correspond to. So let's go ahead and move out of here and create these variables. Transform, recode into different variables, this is how we're going to start our process of
- 11. creating the dummy variables. Because we are creating new variables. So SPSS is asking, what's the input variable? You think of that as the original variable, country by region. Because we are going to pull this apart. So country by region is our original variable. Now let's create our first dummy variable, we'll call it West Africa. © 2016 Laureate Education, Inc. 1
- 12. Dummy Variables And for our label, we'll do the same. So I have to give it old and new values. So the old value for West Africa was 1, and the new value is going to be 1. And for dummy variables, they have to take on the attribute value of either 1 or 0. 1 it has a attribute, or 0 it doesn't. And hopefully that becomes just a little bit clearer as we walk through this process. Now since I'm creating this dummy variable for West Africa, I've already told SPSS from that original variable, country by region, take all the West Africa cases and essentially flip that switch, turn them on to create this new West Africa dummy variable. All others turn off. Those are not West Africa. So there are a couple different ways you can do that. I'm going to show you the what I would call quote, unquote the long way of doing this. So if we have to, remember we had three other groups to this variable. We had the old value of 2, which corresponded to East Africa, that's now going to be a 0. We had 3 which was southern Africa. Again, for our West Africa variable, it's going to be 0. Don't forget to hit add. In then four, North Africa, which is our reference category, 0. Add. Now I could go ahead I could use the range. You know I could
- 13. have just done 2 through 4 equals 0. That would have worked. Or I could've also done all other values and then put the new value in of zero. So that would have told SPSS, OK, take 1 equals 1. All others 0. The only thing to be just a little cautious about there it is if you have user defined or system defined missing values. They could possibly be thrown in there. Again, it depends upon this specific data set and how things are coded in there. So that's why I'm just showing you what I call quote unquote the long way of doing it today. Go ahead click continue. Be sure and hit this radio icon change. Once you hit that, you'll see the OK is sort of activated. We can go ahead and create that variable. We'll see we'll get some SPSS syntax output here. And there it is. It says our variables been created. OK, so here it is West Africa. Now we need to create two other dummy variables so that we have our three dummy variables here. So let's go ahead and see if we can quickly do this. So recode into different variables. One thing I always do is hit reset because everything you did before is still going to be in there, so I just do this so I don't confuse myself. Again, doing the same thing, country by region. Except this one I'm calling East Africa because I'm creating a separate dummy variable for East
- 14. Africa. OK, old and new value, so our old value for East Africa was 2. Now the new value is going to be 1. Remember dummy variables have to have the value 1, it has an attribute, or 0. So I'm saying, OK, all East Africa cases now turn into 1 for this dummy variable of the East Africa. Add. And 1, which was West Africa, is now going to be 0. I mean everything else is going to be 0, all others 0. © 2016 Laureate Education, Inc. 2
- 15. Dummy Variables Again four our reference category, and our reference category is going to be 0 in each of them. Hit continue. Sure, again, hit change. If you don't hit change, you'll see that OK will not sort of light up, if you will, for you. You have to go ahead, and there we go. Hit OK. And there's our output, it's been created. And one more. Recode into different variables, reset, again, country by region, our final variable, which is Southern Africa. Old and New value, so in the old value, the original country by region that was coded as a 3, and now it's going to be coded as 1 because we're focusing on that Southern Africa dummy variable, add. And all others 0. And make sure we get our reference North Africa in here, 0. Change. OK. So now we can see we have West Africa, East Africa, and Southern Africa set up as dummy variables. And if we go click down here, if we go to our data view, you'll see our original variable, country by region, so 1, remember 1, in the original variable corresponded to West Africa. And if we go over here and look at our West Africa variable, you see that for those cases where the original variable was 1, coded West Africa, is now also 1 for the West Africa
- 16. dummy variable but 0 for East and Southern Africa. And so if we go ahead and scroll down to East Africa, so here we go. So for cases where our original variable country by origin 2, remember that equaled East Africa, and still does in the original variable. But now if we go over to West Africa, 0, it's not West Africa, 1. It is East Africa. So for this dummy variable those things are matching up which is a good thing. And 0 for Southern Africa. Again, remember North Africa is serving as our reference category. So now we've created dummy variables, we can go ahead and use them in a linear regression analysis. So let's just go ahead and run a very quick linear regression. So I've gone ahead and already entered those variables in here. I'm just going to use, we don't have many variables to work with, so we're just going to trust and government as our dependent variable. And only use these, again, just for the sake of demonstration these categorical dummy variables as independent variables. Click OK. So by this point, you're probably very familiar with the output around model summary and the ANOVA, let's go ahead and look at the coefficients. You'll see here now that we have each of these dummy variables represented. And so we can go ahead and interpret these coefficients, these un-
- 17. standardized coefficients. And what these un-standardized coefficients are representing is a value in reference to the reference category, to North Africa. So for instance, West Africa, the un-standardized coefficient there, 1.289, that is saying compared to North Africa, there's a difference in West Africa of 1.289 units or our dependent variable is trust in government measured on this index. © 2016 Laureate Education, Inc. 3 Dummy Variables So there's a difference in trust in government of 1.289 units on that index compared to North Africa. And we can go and an interpret the same for East Africa and southern Africa, those un-standardized coefficients are in comparison to the North Africa means. So it's the West Africa mean for trust in government being compared to the North Africa mean. So it's really what we're looking at here is the difference between
- 18. those means of West Africa, North Africa, East Africa, and North Africa, and Southern Africa, and North Africa, again, the means. And that's how you create dummy variables in SPSS. © 2016 Laureate Education, Inc. 4