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how to interpret interaction effects in negative binomial model

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how to interpret interaction effects in negative binomial model

WANG Shiheng
Dear all,

I have a question about how to interpret the interaction items in negative
binomial regression.

In the following model “post” is a dummy variable (0 or 1) to indicate two
different periods (0 represents the first period, 1 represents the second
period).  “treatment” is a dummy variable (0 or 1) to indicate two
different groups –“treatment sample”(1) vs. “control sample” (0). The
interaction is the product of the two dummies. The dependent variable is
the number of analysts. My research objective is to examine whether the
number of analysts changes over the two periods, and whether the changes
over periods differ between the treatment sample and control sample.

I have the following questions for the estimates below:

(1) the coefficient on "post" is not significant, does this mean that the
change in the number of analysts from period 1 to period2 is not
statistically significant in the control group?

(2) the coefficient on the interaction term "post*treatment" is
significantly positive, does this mean that the change in the number of
analysts from period 1 to period2 is significantly greater in the
treatment sample than the control sample? How to interpret the coefficient
on the interaction term exactly? How can I calculate if the changes in
number of analysts from period 1 to period 2 differ between the treatment
sample and control sample?


Negative binomial regression                   Number of obs   =      30274
Dispersion = mean                               Wald chi2(37)   =          .
Log pseudolikelihood = -27412.392              Prob > chi2     =          .

                                                                                                            (Std.
Err.
adjusted
for
45
clusters
in
n)
---------------------------------------------------------------------------
           |             Robust
 Analysts  |    Coef.    Std. Err.     z     P>|z|   [95% Conf. Interval]
-----------+-------------------------------------------------------------
post          .0610886  .0743914     0.82   0.412   -.0847159    .2068931
treatmen     -2.975135  .1591135   -18.70   0.000   -3.286992   -2.663278
post*treatment .214007  .0730457     2.93   0.003    .0708402    .3571739
---------------------------------------------------------------------------

Your help is greatly appreciated.

--

Shiheng Wang

Assistant Professor
Department of Accounting
School of Business and Management
Hong Kong University of Science and Technology

Tel: 852 2358 7570
Fax: 852 2358 1693
Email: [hidden email]

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Re: how to interpret interaction effects in negative binomial model

Maarten buis
--- On Tue, 23/3/10, WANG Shiheng wrote:

> I have a question about how to interpret the interaction
> items in negative binomial regression.
>
> In the following model “post” is a dummy variable (0 or
> 1) to indicate two different periods (0 represents the
> first period, 1 represents the second period). 
> “treatment” is a dummy variable (0 or 1) to indicate two
> different groups –“treatment sample”(1) vs. “control
> sample” (0). The interaction is the product of the two
> dummies. The dependent variable is the number of analysts.
<snip>
>               coef       se
> post          .0610886  .0743914    
> treatmen     -2.975135  .1591135
> post*treatment .214007  .0730457

I would analyse these results in terms of incidence rate
ratios, by adding the -irr- option. You can do it also by
hand, by computing irr = exp(coef) (but why do it yourself
if Stata can do it for you?). The basic logic behind this
type of interpretation of interaction terms in non-linear
models is discussed here:
http://www.maartenbuis.nl/wp/interactions.html

To come back to your case:

The expected number of analysist in the non-treatment group
increases by a factor exp(.061)= 1.06 (i.e. 6%) when a firm
went from the pre-period to the post-period. This ratio is
however not significant. [1]

This effect of post increases by a factor of exp(.214) =
1.24 (i.e. 24%) if the firm is in the treatment group. This
change in effect is significant. [1]

The expected number of analysists in the pre-period group
changes by a factor of exp(-2.975) = .05 (i.e. a change of
-95%) when a firm receives the treatment. This effect is
significant. [1]

This effect of treatment changes by a factor of exp(.214) =
1.24 (i.e. the effect becomes 24% less negative) in the
post-period. This effect is significant. [1]

Hope this helps,
Maarten

[1] It may come as a surprise that I use the test that
coef = 0 to test the hypothesis that exp(coef) = 1. The
logic behind this choice is discussed here:
http://www.stata.com/support/faqs/stat/2deltameth.html

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------



     

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Re: how to interpret interaction effects in negative binomial model

WANG Shiheng
Thank you very much! This is helpful.

Regards,

Shiheng


> --- On Tue, 23/3/10, WANG Shiheng wrote:
>> I have a question about how to interpret the interaction
>> items in negative binomial regression.
>>
>> In the following model “post” is a dummy variable (0 or
>> 1) to indicate two different periods (0 represents the
>> first period, 1 represents the second period). 
>> “treatment” is a dummy variable (0 or 1) to indicate two
>> different groups –“treatment sample”(1) vs. “control
>> sample” (0). The interaction is the product of the two
>> dummies. The dependent variable is the number of analysts.
> <snip>
>>               coef       se
>> post          .0610886  .0743914
>> treatmen     -2.975135  .1591135
>> post*treatment .214007  .0730457
>
> I would analyse these results in terms of incidence rate
> ratios, by adding the -irr- option. You can do it also by
> hand, by computing irr = exp(coef) (but why do it yourself
> if Stata can do it for you?). The basic logic behind this
> type of interpretation of interaction terms in non-linear
> models is discussed here:
> http://www.maartenbuis.nl/wp/interactions.html
>
> To come back to your case:
>
> The expected number of analysist in the non-treatment group
> increases by a factor exp(.061)= 1.06 (i.e. 6%) when a firm
> went from the pre-period to the post-period. This ratio is
> however not significant. [1]
>
> This effect of post increases by a factor of exp(.214) =
> 1.24 (i.e. 24%) if the firm is in the treatment group. This
> change in effect is significant. [1]
>
> The expected number of analysists in the pre-period group
> changes by a factor of exp(-2.975) = .05 (i.e. a change of
> -95%) when a firm receives the treatment. This effect is
> significant. [1]
>
> This effect of treatment changes by a factor of exp(.214) =
> 1.24 (i.e. the effect becomes 24% less negative) in the
> post-period. This effect is significant. [1]
>
> Hope this helps,
> Maarten
>
> [1] It may come as a surprise that I use the test that
> coef = 0 to test the hypothesis that exp(coef) = 1. The
> logic behind this choice is discussed here:
> http://www.stata.com/support/faqs/stat/2deltameth.html
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://www.maartenbuis.nl
> --------------------------
>
>
>
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>


--

Shiheng Wang

Assistant Professor
Department of Accounting
School of Business and Management
Hong Kong University of Science and Technology

Tel: 852 2358 7570
Fax: 852 2358 1693
Email: [hidden email]

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
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