st: Testing for significant differences between groups after running a random-effects regression

[Michael Housman <mhousman@evolvondemand.com>]

Hi folks,

Was wondering if anyone could tell me how to test for significant differences between groups after running a random-effects regression?

By way of background, I have data in which each observation represents an employee-date and the dependent variable is a performance metric (e.g., average handle time, customer satisfaction, etc.) for call center agents.  In essence, I'm trying to model performance and plot the learning curve as a function of "day_of_service" for four different groups of employees.

I've generated a variable called "hire_score_order" that's numbered 1 to 4, representing the four different groups that I want to represent.  I've interacted that term twice with day_of_service so I can visually represent the first- and second-order effects.  I've copied below my "xtreg" command and the resulting output for a sample metric.

What I want to do is run xtreg post-estimation to test the hypothesis that group 1's learning curve is significantly different than groups 2's, group 2's vs. group 3's, etc.  Any suggestions?

Thanks in advance!

Best,
Mike



xtreg aht c.day_of_service##c.day_of_service##i.hire_score_order, re

Random-effects GLS regression                   Number of obs      =    242792
Group variable: emp_id                          Number of groups   =      1984

R-sq:  within  = 0.0049                         Obs per group: min =         1
       between = 0.1248                                        avg =     122.4
       overall = 0.0622                                        max =       500

                                                Wald chi2(38)      =   1544.57
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

--------------------------------------------------------------------------------------------------------------------
                                               aht |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------------------------------+----------------------------------------------------------------
                                    day_of_service |  -.0035472   .0302398    -0.12   0.907    -.0628162    .0557218
                                                   |
                 c.day_of_service#c.day_of_service |  -9.38e-07   4.63e-06    -0.20   0.839      -.00001    8.13e-06
                                                   |
                                  hire_score_order |
                                                2  |   168.1932   48.20808     3.49   0.000     73.70711    262.6793
                                                3  |   20.51885   68.23659     0.30   0.764    -113.2224    154.2601
                                                4  |   156.1946   109.0574     1.43   0.152    -57.55392    369.9431
                                                   |
                 hire_score_order#c.day_of_service |
                                                2  |  -2.088015   .5027992    -4.15   0.000    -3.073483   -1.102546
                                                3  |  -1.117207   .4928079    -2.27   0.023    -2.083092   -.1513208
                                                4  |  -2.408916   1.294864    -1.86   0.063    -4.946802    .1289699
hire_score_order#c.day_of_service#c.day_of_service |
                                                2  |   .0023866   .0016018     1.49   0.136    -.0007529    .0055262
                                                3  |   .0014925   .0014822     1.01   0.314    -.0014126    .0043976
                                                4  |   .0040321   .0037677     1.07   0.285    -.0033524    .0114167
                                                   |
                                             _cons |   246.4581   81.31057     3.03   0.002     87.09236    405.8239
---------------------------------------------------+----------------------------------------------------------------
                                           sigma_u |  521.47501
                                           sigma_e |  930.20434
                                               rho |  .23912442   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------------------------------


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