*Application: Multivariate modeling

Procedure:

Provide a brief description of the procedure for generating a multivariate model (linear regression for interval dependent variable, binary logistic regression for binary dependent variable, or ordinal logistic regression for ordinal dependent variable). Your description should include 1) the R command and statistical procedure used, and 2) the raw output presented by R. The purpose of this section is to a) verify that you have selected the appropriate procedure, b) verify that you have completed and interpreted the procedure correctly, and c) document these procedures in your own way for future use on other projects.

To complete this assignment, you will report on the one best multivariate model for your part of the group project (even if your group decides not to use it).

Writeup:

Write the results of your analysis in paragraph form. The writeup should achieve the following:

• Identify the substantive results of the analysis
• Provide the technical results, with emphasis on the substantive meaning of those results (z-scores, t-scores, and p-values can be reported in parentheses). "Technical results" consists of the model run and the variables used, as well as interpretations for each statistically significant independent variable (including slope or factor change coefficient as appropriate). Indicate variables that are not statistically significant all at once and state the alpha value or confidence level (you can do these in parentheses).
• Identify conclusions or implications of the results relative to the research question(s) addressed by the analysis.

Example Writeup (this one is based on an ordinal logistic regression):

Three factors affect public employee confidence in public agencies:  Improvement of products and services based on public/customer input, incentive programs that inspire employees to do their best, and overall satisfaction with the organization. These findings result from an ordinal logistic regression model predicting the level of employee confidence in the ability of their own government agency to compete with private firms.  Employee confidence was measured on an ordinal scale from 1 (low confidence) to 5 (high confidence).

Where public employees believe that products and services are improved based on public or customer input, the predicted probability of believing that the employee's agency could compete with private firms increases by a factor of 1.5, holding all other variables constant (z=5.24, p<.001).

While incentive programs are an important predictor of public employee confidence in federal agencies, some specific kinds of rewards did not have an impact. Awards programs that “provides [them] with an incentive to do [their] best” increase the predicted probability of agreeing with the comparative confidence statement by a factor of 2.5, holding all other variables constant (z=10.74, p<.001).  Merit programs significantly increase the predicted probability of agreeing with the confidence statement for supervisors and non-supervisors, but not for executives. Benefits programs had no significant effect on the general population of respondents, nor on any of the subgroups. Pay had a small effect on the whole group (z=1.77, p<.1), but did not significantly impact any group when the population was divided by supervisory level. Pay was a factor in determining strength of conviction, however, decreasing strength of conviction among both those who agree with the confidence statement (z=-2.37, p<.05), and those who disagree (z=-3.36, p<.001).

Satisfaction in the organization increases the predicted probability of agreeing with the comparative confidence statement in the total respondent population by roughly a factor of 2, holding all other variables constant (z=6.68, p<.001).

These findings suggest that government agencies with incentives programs and with strong client orientations garner greater confidence in the agency's ability to compete. Organizations may be able to gain dual benefit from customer input programs, both by gaining consumer input and confidence and by boosting employee confidence as well. Likewise, incentives programs may simultaneously improve employee performance and employee confidence.