[azzouz cyrine]

Carlo:
the results given by stata 13. are as follows
thank you so much
I do not know if you remember the context of my empirical study.
my questions are :
1)can "rho" argue the use of the logit model with variable effects and not fixed effects?
2)how can I interpret the results?

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
-----------------------------------------------------------------------------------

.

[Carlo Lazzaro]

Azzouz:
thanks for providing the whole stuff within CODE delimiters.
1) likelihood-ratio test outcome is in favour of -xtlogit- vs -logit-. This results has nothing to do with the difference between conditional fixed effect vs random effect specification and cannot say which one specification fits your data better. Moreover, you seem to have a T>N panel dataset (that is, the time-series dimension is larger than the cross-sectional one): if that were the case, I would consider Clustering the standard errors of your regerssion on the -panelid- to take autocorrelation into account;;
2) Unfortunately, your -margins- outcome tells you nothing more than the coefficients of -xtlogit- (as you can see, the point estimates are the same).

[azzouz cyrine]

Carlo :
THANKS you .
The purpose of my empirical panel data study is to study the impact of "price volatility" and "trading volume" on the formation of speculative bubbles.
1) I am using logistic regression with variable effects. However, the juries can ask me the question: why did you use the logit model with variable effects and not the logit model with fixed effects?
question: How can I argue the use of logit effects variable and not logit effects fixed?
2) To my knowledge, the "rho" parameter is related to specific effects.
question: can I use the parameter "rho" to justify the use of the logit model with variable effects? or I can use the argument you've explained to me "Moreover, you seem to have a T> N panel dataset (that is, the time-series dimension is larger than the cross-sectional one): if that were the case , I would consider Clustering the standard errors of your regressions on the -panelid-to take autocorrelation into account "
question B:
3) IN FACT as you have already noticed the coefficients of the independent variables "price volatility" and "volume of transactions" have not changed compared to their marginal effects.
I interpreted the results as follows:
- when "price volatility" increases by 1%, the probability that a speculative bubble will be formed is "0 .5548789".
-When the "trading volume" increases by 1%, the probability that a speculative bubble is formed is "6.21e-08".

question: my interpretations, are they correct?

[Carlo Lazzaro]

Azzouz:
thanks for providing further clarifications.
1) & 2) you are using -xtlogit- (not -logit-) to take the panel structure of your data into account. The likelihood-ratio test outcome is in favour of -xtlogit- vs -logit-: hence, your choice is correct given your data. Put differently, a pooled -logit- with standard errors clustered on your -panelid- will not be the way to go, given your data. What the likelihood-ratio test outcome does not tell you is whether -xtlogit- (not logit) with a (conditional) fixed effect specification fits your data better than -xtlogit- with random effect specification. Most part of this choice depends on the customary rule in your research field. Hence, based on the likelihood-ratio test outcome you can justify -xtlogit- vs -logit-but not -re- vs -conditional fe- specification. I would also add that with 50 groups of observations (ie, 50 panels) and a T>N data structure, clustering your standard errors would sound wise.
3) coefficients and margins points estimates are the same because you asked the same question in two different forms. To give an helpful reply about the correctness of your interpretation it would be interesting to know the metrics according to the two predictors were expressed (percentage; continuos variables), In general, you should read each coefficient as the contribution to the variation in the dependent variable for a 1-unit increase in that predictor conditional on the other predictors.
As an aside, I would check whether your regression model gives a fair and true view of the data generating process (that is, if all relevant predictors have been included in the right-hand side of your regression equation). The literature in your research field can hel you out in this respect.

[azzouz cyrine]

1237/5000
Carlo:
I thank you for your professionalism.
1) In fact, you wrote to me "The likelihood-ratio test outcome is in favor of -xtlogit- vs -logit-: hence, your choice is correct given your data."
question: what is the parameter specific to the result of the likelihood test in the results given by the stata software?
2) With regard to the interpretation of the results of the marginal effects, is it in terms of unity or percentage? in other words, whether "price volatility" increases by 1% is correct?
3) you wrote to me. "Hence, based on the likelihood-ratio test outcome you can justify -xtlogit- vs -logit-but not -re-vs -conditional fe-specification.I would also add that with 50 groups of observations (ie, 50 panels) and T> N data structure, clustering your standard errors would sound wise. "
question: I did not understand well.
-How do I justify the coition of the logit model with random effects by referring to the "likelihood-ratio" and how do I interpret this parameter?
-which is the value we must take the "likelihood-ratio", to conclude that it is a logit model with variable effects.
- that means "your standard errors would sound wise."

[Carlo Lazzaro]

Azzouz:
1) & 3) Likelihood-ratio test of rho=0: chibar2(01) = 5274.90 Prob >= chibar2 = 0.000. It's statististical significance means that -xtlogit- outperforms -logit- (and this is enough to justify the correctness of your methodological approach). As replied before, this test cannot, however, provides a justification for choosing -re- specification vs -conditional fe- specification;
2) the interpretation of coefficients expressed in percentage terms may be easier if you multiply them by 100; this way, a 1 unti change of the predicors means 1 perecent change in the dependent variable (see also: https://www.statalist.org/forums/for...tory-variables).
3) as far as clustering standard errors on -panelid- is concerned, my previous suggestion stems from the fact that you have a T>N panel dataset, hence errors autocorreelation can be an issue.

[azzouz cyrine]

Carlo :
as a consequence, I can then justify the choice of the logit model with variable effects against logit model with fixed effects by using its two arguments:
1) This is the panel data such as T> N, which poses a problem of autocorrelation between the residues.
2) The likelihood ratio test of rho = 0: chibar2 (01) = 5274.90 Prob> = chibar2 = 0.000. Its statistical significance means that -xtlogit- surpasses -logit-.
question: if I understand correctly, these 2 arguments are correct and sufficient?

[Carlo Lazzaro]

Azzouz:
1) not quite. T>N calls for clustered standard errors, regardless your choice of going -conditionl fe- or -re-;
2) Correct. The likelihood ratio test of rho = 0: chibar2 (01) = 5274.90 Prob> = chibar2 = 0.000. Its statistical significance means that -xtlogit- surpasses -logit-. This is OK for justifying -xtlogit- vs (pooled) -logit- but does not provide any justification for -re- vs -conditional fe-.
As an aside, please note that there's no such thing as -logit- model with variable effect.