I have estimated a fixed effects model for 4 entities 15 observations on each.
In one model (Model 2), the dependent variable has been subject to a prior logistic transform. 
In model 4, I used the Panel logistic regression fixed effect model in which the dependent variable is transformed within the estimation process. Both re-assuringly produce the same coefficient estimates. However the diagnostics on the test of common intercepts are different. In model 4 there is a significant difference at the 7% level, in model 2 it is clearly non-significant.

Why might these conflicting results arise.?

Model 2: Fixed-effects, using 60 observations
Included 4 cross-sectional units
Time-series length = 15
Dependent variable: logit_RER01

             coefficient   std. error   t-ratio    p-value
  ---------------------------------------------------------
  const      −2.34361      0.168446     −13.91    1.17e-019 ***
  EFFORT      0.0121251    0.00258107     4.698   1.80e-05  ***

Mean dependent var  −1.585677   S.D. dependent var   0.522564
Sum squared resid    7.732874   S.E. of regression   0.374964
LSDV R-squared       0.520034   Within R-squared     0.286351
LSDV F(4, 55)        14.89787   P-value(F)           2.62e-08
Log-likelihood      −23.67039   Akaike criterion     57.34079
Schwarz criterion    67.81251   Hannan-Quinn         61.43685
rho                  0.184053   Durbin-Watson        1.345259

Joint test on named regressors -
  Test statistic: F(1, 55) = 22.0687
  with p-value = P(F(1, 55) > 22.0687) = 1.79828e-005

Test for differing group intercepts -
  Null hypothesis: The groups have a common intercept
  Test statistic: F(3, 55) = 1.76308
  with p-value = P(F(3, 55) > 1.76308) = 0.164948


Model 4: Fixed-effects logistic, using 60 observations
Included 4 cross-sectional units
Time-series length = 15
Dependent variable: RER01
Robust (HAC) standard errors
yhat =~ E(1 / (1 + exp(-X*b)))

             coefficient   std. error   t-ratio   p-value
  -------------------------------------------------------
  const      −2.34361      0.112702     −20.79    0.0002  ***
  EFFORT      0.0121251    0.00180297     6.725   0.0067  ***

Statistics based on the transformed data:

Sum squared resid    7.732874   S.E. of regression   0.374964
LSDV R-squared       0.520034   Within R-squared     0.286351
Log-likelihood      −23.67039   Akaike criterion     57.34079
Schwarz criterion    67.81251   Hannan-Quinn         61.43685
rho                  0.184053   Durbin-Watson        1.345259

Statistics based on the original data:

Mean dependent var   0.181867   S.D. dependent var   0.078366
Sum squared resid    0.195932   S.E. of regression   0.255559
Log-likelihood       96.15616   Akaike criterion    −188.3123

Joint test on named regressors -
  Test statistic: F(1, 3) = 45.2268
  with p-value = P(F(1, 3) > 45.2268) = 0.00671188

Robust test for differing group intercepts -
  Null hypothesis: The groups have a common intercept
  Test statistic: Welch F(3, 28.2) = 2.51034
  with p-value = P(F(3, 28.2) > 2.51034) = 0.0789321







Brian J Revell
Professor Emeritus
Harper Adams University , Shropshire
Current Chair of Defra Economic Advisory Panel
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