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  • Interpretation of coefficients for a multilevel complementary log-log regression - survival analysis

    Dear fellow Stata users,

    i am running a mecloglog model in Stata 17 estimating the transition probabilities of youth from school to vocational education. It is district-level data embedded in greater, local labor market regions, that is why I am using the multilevel. To account for time dependencies my (main) explanatory variable (share_naa_high, a measure for competition depiciting the share of high skilled individuals in a region) is interacted with time (squared), please find my command and regression results below.

    I would like to know, if there is any straightforward interpretation of the coefficients in such a model? Generally of the covariates but specifically here also the one from the interaction c.month_std#c.month_std#c.share_naa_high_std ( -.0663424), as well as if there is any useful interpretation of the singular covariate share_naa_high_std | -.0235111 that is automatically also included when calculating the interaction term.

    My question is potentially rather basic, but I am having trouble finding literature on meclolog or cloglog in general online. I find it mostly mentioned as an alternative to logit etc. but without getting into more detail, especially in terms of regression results. Therefore I would also be happy about any recommendations on textbooks/literature/lectures online etc.

    Thank you ver much,
    Helen

    Code:
     mi estimate, cmdok: mecloglog des2 dig2_std subp_std c.month_std##c.month_std##c.share_naa_high_std $cont || ram: 
    
    Multiple-imputation estimates                   Imputations       =         30
    Mixed-effects cloglog regression                Number of obs     =     31,413
                                                    Average RVI       =     0.0163
                                                    Largest FMI       =     0.1390
    DF adjustment:   Large sample                   DF:     min       =   1,525.20
                                                            avg       =   2.07e+08
                                                            max       =   2.36e+09
    Model F test:       Equal FMI                   F(  14, 1.2e+06)  =      53.97
    Within VCE type:          OIM                   Prob > F          =     0.0000
    
    --------------------------------------------------------------------------------------------------------------
                                            des2 | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
    ---------------------------------------------+----------------------------------------------------------------
                                        dig2_std |   .1385704   .0391823     3.54   0.000     .0617746    .2153662
                                        subp_std |   .0559094   .0441674     1.27   0.206    -.0306571     .142476
                                       month_std |  -.7366246   .0310888   -23.69   0.000    -.7975575   -.6756917
                                                 |
                         c.month_std#c.month_std |   .4431871   .0283443    15.64   0.000     .3876332     .498741
                                                 |
                              share_naa_high_std |  -.0235111   .0667418    -0.35   0.725    -.1543225    .1073004
                                                 |
                c.month_std#c.share_naa_high_std |   .0467641   .0305467     1.53   0.126    -.0131063    .1066346
                                                 |
    c.month_std#c.month_std#c.share_naa_high_std |  -.0663424   .0280888    -2.36   0.018    -.1213955   -.0112893
                                                 |
                                             mig |  -.2895376   .0618225    -4.68   0.000    -.4107121    -.168363
                                          female |  -.2595704     .05484    -4.73   0.000    -.3670549   -.1520859
                                         gpa_std |  -.1108702   .0307685    -3.60   0.000    -.1712232   -.0505172
                                       books_std |   .0612342   .0281863     2.17   0.030     .0059825    .1164858
                                        sltyp_13 |   .0177168   .0865387     0.20   0.838    -.1518959    .1873295
                                                 |
                                      cohort_agg |
                                              2  |  -.2329763   .1035105    -2.25   0.024    -.4358533   -.0300994
                                              3  |  -.3990874   .3874382    -1.03   0.303    -1.158452    .3602776
                                                 |
                                           _cons |  -3.445424   .0786077   -43.83   0.000    -3.599492   -3.291356
    ---------------------------------------------+----------------------------------------------------------------
                                  var(_cons[ram])|   .1268323    .051242                      .0574556    .2799801
    --------------------------------------------------------------------------------------------------------------
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