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  • Alternative analyses to xtologit/xtoprobit for score as dependent variable and dummy as independent variable

    Hi everyone,

    I’m new to Stata (using version 15.1 on Windows 10) and regard my statistical knowledge as rather basic.
    I investigate how firms can take advantage of their investors' assets.
    My data is organized as an unbalanced panel with firm ID as panel variable and report period as time variable. There are 149 firms and 490 observations.

    For my first and second hypotheses my dependent variable is a 0.5-paced score ranging from 0 to 10. My independent variable is a dummy.

    H1:
    Dependent variable: revenues, rev_rating; 0.5-paced score from 0-10
    Independent variable: theoretical fit, theo_fit; dummy, 1 if there is a potential fit between two specific entities, 0 otherwise
    Controls: batch (categorical, 7 options), age (number of months, 23-100), year (controlling for the year in which rating has been performed; categorical, 3 options), status (categorical, 4 options), no_head (size in number of employees, 0-1,100), office (categorical, 12 options)

    H2:
    Dependent variable: rev_rating; 0.5-paced score from 0-10
    Independent variable: cur_fit; dummy; 1 if there is an actual fit between the startup and another entity, 0 otherwise

    Note: theo_fit=1 (independent variable in H1 and upcoming H3) is a prerequisite for cur_fit=1., but not all theo_fit=1 also have cur_fit=1

    I got recommended to run xtologit and compare it with xtoprobit. However, I’m not sure whether this is the right thing to do since my dependent variable is a score rather than a dummy. I cannot run any fixed effects regressions because my independent variable doesn’t change over time and gets omitted. Does someone have other recommendations?

    As an example:

    Code:
    xtologit rev_rating i.theo_fit i.batch months_agreement i.year no_head i.office
    Code:
    Fitting comparison model:
    
    Iteration 0:   log likelihood = -1198.6864  
    Iteration 1:   log likelihood = -1129.2539  
    Iteration 2:   log likelihood = -1124.4294  
    Iteration 3:   log likelihood = -1123.7448  
    Iteration 4:   log likelihood = -1123.7439  
    Iteration 5:   log likelihood = -1123.7439  
    
    Refining starting values:
    
    Grid node 0:   log likelihood = -1083.4717
    
    Fitting full model:
    
    Iteration 0:   log likelihood = -1083.4717  
    Iteration 1:   log likelihood = -1043.0614  
    Iteration 2:   log likelihood = -1037.7987  
    Iteration 3:   log likelihood = -1037.1197  
    Iteration 4:   log likelihood = -1037.1119  
    Iteration 5:   log likelihood = -1037.1119  
    
    Random-effects ordered logistic regression      Number of obs     =        486
    Group variable: id_venture                      Number of groups  =        147
    
    Random effects u_i ~ Gaussian                   Obs per group:
                                                                  min =          2
                                                                  avg =        3.3
                                                                  max =          6
    
    Integration method: mvaghermite                 Integration pts.  =         12
    
                                                    Wald chi2(22)     =      64.83
    Log likelihood  = -1037.1119                    Prob > chi2       =     0.0000
    
    ----------------------------------------------------------------------------------
          rev_rating |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
    -----------------+----------------------------------------------------------------
                     |
          1.theo_fit |   1.667928   .5067086     3.29   0.001      .674797    2.661058
                     |
               batch |
                  2  |  -.9373067   1.107814    -0.85   0.398    -3.108582    1.233968
                  3  |  -2.892619   1.705272    -1.70   0.090    -6.234891    .4496523
                  4  |  -3.495811   2.358969    -1.48   0.138    -8.119304    1.127683
                  5  |  -6.004796   3.021248    -1.99   0.047    -11.92633   -.0832591
                  6  |  -7.476233   3.183285    -2.35   0.019    -13.71536   -1.237108
                  7  |  -9.458639   3.571192    -2.65   0.008    -16.45805    -2.45923
                     |
    months_agreement |  -.1657581   .0721907    -2.30   0.022    -.3072492    -.024267
                     |
                year |
               2016  |   .1925695   .2060094     0.93   0.350    -.2112014    .5963404
               2017  |   .6511408   .3802286     1.71   0.087    -.0940935    1.396375
                     |
             no_head |   .0048509   .0025276     1.92   0.055    -.0001031     .009805
                     |
              office |
                  2  |   2.032175   2.267954     0.90   0.370    -2.412932    6.477282
                  3  |   4.102537    1.47625     2.78   0.005      1.20914    6.995935
                  4  |   2.847437   1.613429     1.76   0.078    -.3148246    6.009699
                  5  |  -1.262037    2.06315    -0.61   0.541    -5.305735    2.781662
                  6  |    2.58405    1.24929     2.07   0.039      .135487    5.032614
                  7  |   3.941555   1.775421     2.22   0.026     .4617931    7.421316
                  8  |   4.322308   1.225161     3.53   0.000     1.921036     6.72358
                  9  |    4.19991   1.351371     3.11   0.002     1.551273    6.848548
                 10  |   1.167777   1.378502     0.85   0.397    -1.534037    3.869591
                 11  |   3.188848   1.320014     2.42   0.016     .6016677    5.776028
                 12  |    3.05598   1.404414     2.18   0.030     .3033797    5.808581
    -----------------+----------------------------------------------------------------
               /cut1 |   -13.3631   6.155648                     -25.42795   -1.298253
               /cut2 |  -12.31746   6.151867                      -24.3749   -.2600186
               /cut3 |  -12.23387   6.151623                     -24.29083   -.1769115
               /cut4 |  -11.42768   6.149416                     -23.48032    .6249499
               /cut5 |  -10.57142   6.146626                     -22.61858    1.475747
               /cut6 |  -10.03098   6.144623                     -22.07422     2.01226
               /cut7 |   -9.96498   6.144372                     -22.00773    2.077769
               /cut8 |  -9.433196   6.142337                     -21.47195    2.605563
               /cut9 |  -9.382367   6.142146                     -21.42075    2.656017
              /cut10 |  -8.348679   6.137557                     -20.37807    3.680712
              /cut11 |   -7.58178   6.134757                     -19.60568    4.442124
              /cut12 |  -7.193055   6.134072                     -19.21561    4.829505
              /cut13 |  -6.611126   6.133662                     -18.63288     5.41063
              /cut14 |   -5.94365   6.133377                     -17.96485    6.077548
              /cut15 |  -5.750003   6.133178                     -17.77081    6.270806
              /cut16 |  -4.813253   6.131405                     -16.83059     7.20408
    -----------------+----------------------------------------------------------------
           /sigma2_u |   5.965185   1.171412                      4.059471    8.765534
    ----------------------------------------------------------------------------------
    LR test vs. ologit model: chibar2(01) = 173.26        Prob >= chibar2 = 0.0000
    Moreover, I got the feeling that my third hypothesis cannot be tested by xtlogit nor xtprobit. Here, both, my dependent (cur_fit) and my independent (theo_fit) variables are dummies moderated by another dummy variable (share_info). 302 observations are not considered (Is that because the independent variable theo_fit doesn't change over time?).

    H3:
    Dependent variable: cur_fit
    Independent variable: theo_fit
    Moderating variable: information sharing, share_info

    I ran

    Code:
    xtlogit cur_fit i.theo_fit##i.share_info
    and get

    Code:
    note: 0.theo_fit != 0 predicts failure perfectly
          0.theo_fit dropped and 302 obs not used
    
    note: 1.theo_fit omitted because of collinearity
    note: 1.theo_fit#1.share_info omitted because of collinearity
    
    Fitting comparison model:
    
    Iteration 0:   log likelihood = -104.60614  
    Iteration 1:   log likelihood = -104.38846  
    Iteration 2:   log likelihood = -104.38808  
    Iteration 3:   log likelihood = -104.38808  
    
    Fitting full model:
    
    tau =  0.0     log likelihood = -104.38808
    tau =  0.1     log likelihood = -99.379343
    tau =  0.2     log likelihood = -94.396503
    tau =  0.3     log likelihood = -89.452781
    tau =  0.4     log likelihood = -84.509089
    tau =  0.5     log likelihood = -79.488327
    tau =  0.6     log likelihood = -74.273074
    tau =  0.7     log likelihood = -68.676386
    tau =  0.8     log likelihood = -62.379474
    
    Iteration 0:   log likelihood = -68.679948  
    Iteration 1:   log likelihood = -35.388335  (not concave)
    Iteration 2:   log likelihood = -35.206976  (not concave)
    Iteration 3:   log likelihood = -35.071197  (not concave)
    Iteration 4:   log likelihood = -35.014527  (not concave)
    Iteration 5:   log likelihood =  -34.90272  (not concave)
    Iteration 6:   log likelihood = -34.746671  (not concave)
    Iteration 7:   log likelihood = -34.608508  (not concave)
    Iteration 8:   log likelihood = -34.498735  (not concave)
    Iteration 9:   log likelihood = -34.498735  (not concave)
    Iteration 10:  log likelihood = -34.417236  (not concave)
    Iteration 11:  log likelihood = -27.688751  (not concave)
    Iteration 12:  log likelihood = -25.901447  
    Iteration 13:  log likelihood = -25.853734  (not concave)
    Iteration 14:  log likelihood = -24.131304  (not concave)
    Iteration 15:  log likelihood = -20.304816  
    Iteration 16:  log likelihood = -19.016582  
    Iteration 17:  log likelihood = -15.744041  
    Iteration 18:  log likelihood = -15.722299  
    Iteration 19:  log likelihood = -15.722287  
    Iteration 20:  log likelihood = -15.722287  
    
    Random-effects logistic regression              Number of obs     =        188
    Group variable: id_venture                      Number of groups  =         55
    
    Random effects u_i ~ Gaussian                   Obs per group:
                                                                  min =          2
                                                                  avg =        3.4
                                                                  max =          6
    
    Integration method: mvaghermite                 Integration pts.  =         12
    
                                                    Wald chi2(1)      =       0.67
    Log likelihood  = -15.722287                    Prob > chi2       =     0.4144
    
    -------------------------------------------------------------------------------------
                cur_fit |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
    --------------------+----------------------------------------------------------------
               theo_fit |
                     0  |          0  (empty)
                     1  |          0  (omitted)
                        |
           1.share_info |   .7869919   .9642079     0.82   0.414    -1.102821    2.676805
                        |
    theo_fit#share_info |
                   0 0  |          0  (empty)
                   0 1  |          0  (empty)
                   1 1  |          0  (omitted)
                        |
                  _cons |  -.4224731    .726772    -0.58   0.561     -1.84692    1.001974
    --------------------+----------------------------------------------------------------
               /lnsig2u |   3.475415   .1946816                      3.093846    3.856984
    --------------------+----------------------------------------------------------------
                sigma_u |   5.684297    .553314                      4.696996    6.879128
                    rho |   .9075908   .0163279                      .8702305    .9349986
    -------------------------------------------------------------------------------------
    LR test of rho=0: chibar2(01) = 177.33                 Prob >= chibar2 = 0.000
    In the end, I made a contingency table to check the frequencies of every possible outcome. Is there another way to analyze it?

    Hope I posted it the right way. If you lack any information let me know.

    Thank you very, very much in advance!
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