Application 8: Multivariate analysis

This assignment should include at least one BIVARIATE test and one MULTIVARIATE test using the SAME DEPENDENT VARIABLE.

Note: If you are using a paired value test as your bivariate test, then use the most recent of the paired values as your dependent variable in the multivariate analysis or justify the use of your bivariate and multivariate tests in the context of your project.

Following is an outline for this week's assignment. Your submission should be written in paragraph form as it might appear in a final report. Outline form is not acceptable for your submission.

1. Purpose of the project (what you are trying to discover).

2. A very brief description of the dependent variable (including level of measurement and an appropriate measure of central tendency)

3. A very brief description of the independent variable (including level of measurement and an appropriate measure of central tendency)

4. A description of how you expect these two variables to be related to each other in a causal relationship and why (provide your reasoning for why your independent variable might cause your dependent variable, if possible, how and why the independent variable could be expected to occur before the dependent variable, etc.)

5. Name the bivariate test you used and say that you used it. Provide a sentence about why.

6. Provide the results from the test and provide the technical interpretation.

7. Provide the substantive interpretation of the test.

8. Describe caveats to your conclusions, including why you might want to include other variables.

9. Identify what multivariate test you use to include other variables, and a sentence about why you are using a multivariate test ( For binary dependent variables, use logistic regression. For most ordinal dependent variables, use ordinal logistic regression. For interval variables, use linear regression.)

10. Present a table containing the variables, regression coefficients, test statistics and p-values. If you are performing logistic regression or ordinal logistic regression, include factor change coefficients (a factor change coefficient is e^b, where e is the natural number and b is the coefficient in your regression output).

11. Interpret the relationships of ALL of the research variables (independent variables you explicitly care about) to your dependent variable.

12. Interpret the relationships of the statistically significant control variables (independent variables you include only to rule out spurious relationships) to your dependent variable.

13. Report and interpret the R-squared value, adjusted R-squared value, if appropriate (if it's reported, it's appropriate).

14. Discuss the regression results, answering the substantive questions raised in part 1 and providing any relevant conclusions or implications from this analysis. What further questions might need to be addressed? What variables were not included that should have been? Be brief--you can go into more detail in your final report. Do be careful not to overreach your data.

Example writeup:

The purpose of this analysis is to determine whether or not marital status has an impact on homeownership status. Homeownership status is derived from the Spanish Fork citizen satisfaction survey, which reads "Please indicate your homeownership status" with the options "own" and "rent/lease" and "other" as options. Those who indicated that they own their home were coded as 1 and those who indicated one of the other two options were coded as 0. In our sample, 32 percent of survey respondents indicated that they own their own home. Marital status is derived from a question on the same survey, which reads "please indicate your marital status." Options included "married," "single," "divorced," and "widowed." Those who indicated that they were married were coded 1 and all others were coded 0.

We expect marital status to have a stabilizing effect on the desire and ability to own a home. Therefore, we expect a positive correlation between being married and owning a home. We expect that many Spanish Fork residents do not purchase homes until after they marry, and that marriage makes them more interested in home ownership.

It appears that marriage does, in fact, impact homeownership status. Because both variables, marrital status and homeownership status, are binary, we performed a two-group proportion test to determine whether or not there is a correlation between marital status and homeownership. The test suggests that there is a positive correlation between marital status and homeownership. On average, about 6.3 percent more married people indicated that they owned their own home than did non-married people (chi-square = ENTER VALUE, p<0.001 for a two-tailed test).

These results suggest support for our hypothesis about marriage and homeownership, but there may be other factors at play. For example, people are more likely to be married as they age, and are also more likely to be employed and to have more income. It may be that the marriage variable is really capturing these other variables in the bivariate analysis.

We examined the same question by using a binary logistic regression to examine the impact of marriage on homeownership status, controlling for age (ordinal), income (ordinal), and employment status (1= employed, 0=not employed). The results of this analysis are presented in table 1.

Table 1: Results from Logistic Regression of Homeownership (1= homeowner, 0=not homeowner)

In the multivariate analysis, it is clear that marriage itself does not correlate with homeownership status (p>0.05). However, it appears that age and income have positive impacts on the likelihood of owning a home. Specifically, a one-level increase in income makes a respondent about 3.3 times more likely to own their own home (f=1.74, p=0.04), and a one level increase in age makes respondents almost 3 times more likely to own their own home(f=2.01, p=0.02).

These results suggest that age and income are more important factors than marriage in predicting homeownership among residents. Future analysis should examine additional factors such as family size, asset wealth, and location on homeownership status.