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

 From Michael Housman To "statalist@hsphsun2.harvard.edu" Subject st: Testing for significant differences between groups after running a random-effects regression Date Tue, 9 Oct 2012 15:57:00 +0000

```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?

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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