How to interpret output (sigma_u and rho) from Stata’s xtlogit command?

[Monzur Alam]

Dear all,

I am trying to estimate a random intercepts model, using the xtlogit command in Stata 14. Coll_action is a binary dependent variable, where 1 means that an individual engages in collective action. Pp_num1 is the group variable which denotes the neighborhood. educ2 educ3 educ4 educ5 relgn_muslim are individual level variables, and lowinc_housing_census is a neighborhood level variable that indicates the proportion of households with low income in the neighborhood.


I was wondering how to interpret the sigma_u and rho (intraclass correlation) in the models, and look forward to any suggestions.

//model 1, intercept only
. xtlogit coll_action, i(ppnum_1) re  vce(robust) 
 
 
 
Calculating robust standard errors:
 
Random-effects logistic regression              Number of obs     =      3,983
Group variable: ppnum_1                         Number of groups  =        200
 
Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =       19.9
                                                              max =         56
 
Integration method: mvaghermite                 Integration pts.  =         12
 
                                                Wald chi2(0)      =          .
Log pseudolikelihood  = -2565.3776              Prob > chi2       =          .
 
                              (Std. Err. adjusted for 200 clusters in ppnum_1)
------------------------------------------------------------------------------
             |               Robust
 coll_action |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |  -.6085705   .0585815   -10.39   0.000    -.7233881    -.493753
-------------+----------------------------------------------------------------
    /lnsig2u |  -.9666286   .1958436                     -1.350475   -.5827822
-------------+----------------------------------------------------------------
     sigma_u |    .616736   .0603919                      .5090355    .7472234
         rho |   .1036347   .0181928                      .0730116    .1450915
------------------------------------------------------------------------------
 
 
//model 2, adding individual level variables
 
. xtlogit coll_action educ2 educ3 educ4 educ5 relgn_muslim , i(ppnum_1) re  vce(robust)
 
 
Calculating robust standard errors:
 
Random-effects logistic regression              Number of obs     =      3,983
Group variable: ppnum_1                         Number of groups  =        200
 
Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =       19.9
                                                              max =         56
 
Integration method: mvaghermite                 Integration pts.  =         12
 
                                                Wald chi2(5)      =       7.92
Log pseudolikelihood  = -2560.3897              Prob > chi2       =     0.1608
 
                              (Std. Err. adjusted for 200 clusters in ppnum_1)
------------------------------------------------------------------------------
             |               Robust
 coll_action |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       educ2 |  -.2358874   .2471499    -0.95   0.340    -.7202923    .2485176
       educ3 |   .1068126    .137044     0.78   0.436    -.1617886    .3754139
       educ4 |  -.0034217   .1208636    -0.03   0.977      -.24031    .2334666
       educ5 |   .0389941   .1312138     0.30   0.766    -.2181803    .2961684
relgn_muslim |   .2761378   .1213664     2.28   0.023     .0382641    .5140115
       _cons |   -.678434   .1210602    -5.60   0.000    -.9157076   -.4411603
-------------+----------------------------------------------------------------
    /lnsig2u |  -.9823252   .1915234                     -1.357704   -.6069463
-------------+----------------------------------------------------------------
     sigma_u |   .6119146    .058598                      .5071989    .7382497
         rho |   .1021856   .0175711                      .0725239    .1421198
------------------------------------------------------------------------------
//model 2, adding neighborhood level variables
 
 
. xtlogit coll_action educ2 educ3 educ4 educ5 relgn_muslim lowinc_housing_census, i(ppnum_1) re  vce(robust) 
 
 
 
Calculating robust standard errors:
 
Random-effects logistic regression              Number of obs     =      3,983
Group variable: ppnum_1                         Number of groups  =        200
 
Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =       19.9
                                                              max =         56
 
Integration method: mvaghermite                 Integration pts.  =         12
 
                                                Wald chi2(6)      =       9.04
Log pseudolikelihood  = -2560.1952              Prob > chi2       =     0.1715
 
                                       (Std. Err. adjusted for 200 clusters in ppnum_1)
---------------------------------------------------------------------------------------
                      |               Robust
          coll_action |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
                educ2 |  -.2361818   .2471599    -0.96   0.339    -.7206062    .2482427
                educ3 |   .1041136    .136647     0.76   0.446    -.1637096    .3719369
                educ4 |   -.011128   .1194828    -0.09   0.926      -.24531    .2230539
                educ5 |   .0254471   .1299225     0.20   0.845    -.2291962    .2800905
         relgn_muslim |   .2785445   .1209994     2.30   0.021       .04139     .515699
lowinc_housing_census |  -.1507785   .2571716    -0.59   0.558    -.6548256    .3532685
                _cons |  -.6423424   .1266259    -5.07   0.000    -.8905246   -.3941602
----------------------+----------------------------------------------------------------
             /lnsig2u |  -.9893431   .1886524                     -1.359095   -.6195911
----------------------+----------------------------------------------------------------
              sigma_u |   .6097712   .0575174                      .5068463    .7335969
                  rho |   .1015435   .0172112                      .0724303    .1405851
---------------------------------------------------------------------------------------

[Carlo Lazzaro]

Monzur:
-sigma_u- is the panel-level variance;
-rho- is the intraclass correlation, that is: (sigma_u/(sigma_u+sigma_e)), where sigma_e is the unit-level variance.
That said, why not using -meqrlogit-?

[Monzur Alam]

Thank you Carlo. I will try out the meqrlogit command.

[azzouz cyrine]

bonsoir , je suis en train d'étudier l'effet de la volatilité des prix et du volume de transactions sur la formation de bulle spéculative sur un marché boursier ( est une variable binaire) via le modéle logit à effets variable .
les résultats sont les suivants :
Random-effects logistic regression Number of obs = 65955
Group variable: codeentreprise Number of groups = 50

Random effects u_i ~ Gaussian Obs per group: min = 337
avg = 1319.1
max = 2727

Integration method: mvaghermite Integration points = 12

Wald chi2(2) = 4479.17
Log likelihood = -7270.5549 Prob > chi2 = 0.0000

-----------------------------------------------------------------------------------
Bulle | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
Volatilitdesprix | .5548789 .0082921 66.92 0.000 .5386267 .5711311
QUANTITE_NEGOCIEE | 6.21e-08 4.88e-08 1.27 0.204 -3.36e-08 1.58e-07
_cons | -7.049741 .1296784 -54.36 0.000 -7.303906 -6.795576
------------------+----------------------------------------------------------------
/ lnsig2u | 3.058475 .2787318 2.512171 3.604779
------------------+----------------------------------------------------------------
sigma_u | 4.614657 .6431258 3.511648 6.064122
rho | .8661836 .0323077 .7894018 .9178835
-----------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 5274.90 Prob >= chibar2 = 0.000


mes questions sont :
1) est ce qu'il faut calculer l'effet marginale du chaque variable explicative afin de pouvoir interpréter leurs effets sur la formation du bulle ? , si oui , comment puisse je le faire ?
2) quel est l'utilité du : / lnsig2u , sigma_u , et rho ?
3) comment puisse je les interpréter : ( / lnsig2u , sigma_u , et rho ?) ?

[azzouz cyrine]

Dear all , I am studying the volatility of prices and transactions on speculative bubble formation on a stock market by the logit model with variable effects.
the results are as follows:

Random-effects logistic regression Number of obs = 65955
Group variable: codeentreprise Number of groups = 50

Random effects u_i ~ Gaussian Obs per group: min = 337
avg = 1319.1
max = 2727

Integration method: mvaghermite Integration points = 12

Wald chi2(2) = 4479.17
Log likelihood = -7270.5549 Prob > chi2 = 0.0000

-----------------------------------------------------------------------------------
Bulle | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
Volatilitdesprix | .5548789 .0082921 66.92 0.000 .5386267 .5711311
QUANTITE_NEGOCIEE | 6.21e-08 4.88e-08 1.27 0.204 -3.36e-08 1.58e-07
_cons | -7.049741 .1296784 -54.36 0.000 -7.303906 -6.795576
------------------+----------------------------------------------------------------
/ lnsig2u | 3.058475 .2787318 2.512171 3.604779
------------------+----------------------------------------------------------------
sigma_u | 4.614657 .6431258 3.511648 6.064122
rho | .8661836 .0323077 .7894018 .9178835
-----------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 5274.90 Prob >= chibar2 = 0.000


my questions are:
1) is it necessary to calculate the marginal effect of each explanatory variable in order to be able to interpret their effects on the formation of the bubble? if so, how can I do it?
2) what is the usefulness of: / lnsig2u, sigma_u, and rho?
3) how can I interpret them: (/ lnsig2u, sigma_u, and rho?)?

[Carlo Lazzaro]

Azzouz:
- please use CODE delimiters to share what you typed and what Stata gave you back (see the FAQ). Thanks.
1) if you mean the contribution of each predictor when adjusted for the remaining ones, you can read it in the -xtlogit- outcome table; if you mean something different, see -help margins- and -help marginsplot-;
2) and 3): please see -xtlogit- entry in Stata .pdf manual.

As an aside, I would check whether all the predictors related to the data generating processa have been included in the right-hand side of your regerssion equation.

[azzouz cyrine]

thanks carlo and I apologize for the anomaly.
another question, how to interpret the results of the marginal effect?

[Carlo Lazzaro]

Azzouz:
sorry for providing a general advice, but quoting from -help margins-

Margins are statistics calculated from predictions of a previously fit model at fixed values of some covariates and averaging or otherwise integrating over the remaining covariates.

you can easily envisage that any helpful reply is conditional on knowing what you'after (namely which "margin" you're interested in).

[azzouz cyrine]

Carlo:
I am studying the effect of x on y such that:
x: the varioable independent, quantitative
y: the dependent variable, qualitative = dichotomous variable
I used logic regression and then I determined the marginal effect of x on y.
the result: DY / X: 0.0866433
I interpreted the result as follows:
when x increases by 1%, the probability of occurrence of Y
is 0.0866433.
my question: Is this interpretation correct?

[Carlo Lazzaro]

Azzouz:
the best way to increase your chances of getting helpful replies is to post what you typed and what Stata gave you back via CODE delimiters (please see the FAQ on this and other posting-related topics. Thanks).

[azzouz cyrine]

Carlo :
I am using the xtlogit command in stata 13.1. Bubble, is the dependent variable that takes the value 1 when the speculative bubble is formed on the Tunsian stock market and 0 if not. price volatility and trading volume are the independent variables and are quantitative.
To interpret the results I used the command margins, dydx (*) atmeans in stata 13.1.
the results provided by STATA are presented by the word document below.
I apologize if I did not accept the rules of the FORUM for lack of time.
thanks for your help.

[Carlo Lazzaro]

Azzouz:
sorry to refer you again to FAQ, but attaching Stata which are not in Stata format is not the way to go, as most on this list (me too) do not download a file from unknown source due to the risk of active contents.
Again the best approach is to use CODE delimiters (FAQ again): if you do not have time to follow Stata forum rules, it may happen that even potentially interested listers decide that they have no time to reply to your queries.
That said, apparently you have calculated the derivatives of the responses of your covariates at their mean. Please see example 17 and 18 under -margins- entry in Stata .pdf manual.

[azzouz cyrine]

CARLO:
I'm sorry again and you're right.
When I tell you that I do not have time it's just because I need a quick answer and I'm in a hurry. I did not get to learn the rules of the forum. for example, I did not understand how I postulate my results given by the STATA software, how I use "CODE delimiters".
I will read the "FAQ" again.
thank you so much

[Carlo Lazzaro]

Azzouz:
I'm obviously simphatetic with those (like me and, I believe, all on this forum), but learning how to use CODE delimiters is very easy:
- click on the toggle advanced editor (A) on the upper-right side of the posting/replying space;
- then click on the #shaped toggle;
- put what you typed and what Stata gave you back in between;
- congrats'! you did it!

[azzouz cyrine]

Random-effects logistic regression              Number of obs      =     65955
Group variable: codeentreprise                  Number of groups   =        50

Random effects u_i ~ Gaussian                   Obs per group: min =       337
                                                               avg =    1319.1
                                                               max =      2727

Integration method: mvaghermite                 Integration points =        12

                                                Wald chi2(2)       =   4479.17
Log likelihood  = -7270.5549                    Prob > chi2        =    0.0000

-----------------------------------------------------------------------------------
            Bulle |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
 Volatilitdesprix |   .5548789   .0082921    66.92   0.000     .5386267    .5711311
QUANTITE_NEGOCIEE |   6.21e-08   4.88e-08     1.27   0.204    -3.36e-08    1.58e-07
            _cons |  -7.049741   .1296784   -54.36   0.000    -7.303906   -6.795576
------------------+----------------------------------------------------------------
         /lnsig2u |   3.058475   .2787318                      2.512171    3.604779
------------------+----------------------------------------------------------------
          sigma_u |   4.614657   .6431258                      3.511648    6.064122
              rho |   .8661836   .0323077                      .7894018    .9178835
-----------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =  5274.90 Prob >= chibar2 = 0.000

. margins, dydx (*) atmeans

Conditional marginal effects                      Number of obs   =      65955
Model VCE    : OIM

Expression   : Linear prediction, predict()
dy/dx w.r.t. : Volatilitdesprix QUANTITE_NEGOCIEE
at           : Volatilitd~x    =    .5302004 (mean)
               QUANTITE_N~E    =    15138.75 (mean)

-----------------------------------------------------------------------------------
                  |            Delta-method
                  |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
 Volatilitdesprix |   .5548789   .0082921    66.92   0.000     .5386267    .5711311
QUANTITE_NEGOCIEE |   6.21e-08   4.88e-08     1.27   0.204    -3.36e-08    1.58e-07
-----------------------------------------------------------------------------------

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