Fixed effects conditional logit model, problems with Age and Year's effect

[Alessandro Gallo]

Hello everyone,

I am using unbalanced panel data on individual respondents (T = 11 and N = 83687). I am running a conditional logit model with fixed effects, the dependent variable it's a dummy (at time t) and I run most of the covariates with a lag of one year in (t-1).
I'm using regional (i.region) and year's effects (i.syear). My problem is due to convergence. If I run the fixed effects conditional logit model with all the year's effects (i.syear) and the covariates Age and Age² (using squared Age to model the age effect) I get no convergence. Therefore, considering that I got no standard errors (.) in the year effect 2019, I tried to create myself a dummy variable for each year I'm considering and I excluded the year 2019 effect (because I thought there were not enough observations to achieve the convergence). In that case, it works fine and the convergence it's achieved.

Moreover, I tried to consider instead of Age and Age² some Age Categories ( 5 categories). With the Age categories everything it's working fine and the convergence it's achieved considering all the year's effects (by using i.syear).

I think I will probably consider the Age categories model for my final version but I was wondering why was the convergence not achieved when considering the Age and Age² and all the year's effects (i.syear) and on the contrary, it was when considering the Age categories and all the year's effects?

here there is the code:

. xtlogit resigning L.insecurity L.ln_income i.region i.syear L.age L.age2 i.L.married i.L.health_status1    L.ye
> ars_of_education L.n_of_children L.annual_working_hours, fe iterate(20)
note: multiple positive outcomes within groups encountered.
note: 12,229 groups (50,752 obs) omitted because of all positive or
all negative outcomes.

Iteration 0:   log likelihood = -4954.8824  (not concave)
Iteration 1:   log likelihood = -4923.8604  (not concave)
Iteration 2:   log likelihood = -4918.2668  (not concave)
Iteration 3:   log likelihood = -4917.9681  (not concave)
Iteration 4:   log likelihood = -4917.8448  (not concave)
Iteration 5:   log likelihood = -4917.7838  (not concave)
Iteration 6:   log likelihood = -4917.6602  (not concave)
Iteration 7:   log likelihood = -4917.6032  (not concave)
Iteration 8:   log likelihood = -4917.3976  (not concave)
Iteration 9:   log likelihood = -4917.3279  (not concave)
Iteration 10:  log likelihood = -4917.3174  (not concave)
Iteration 11:  log likelihood = -4917.3072  (not concave)
Iteration 12:  log likelihood = -4917.2688  (not concave)
Iteration 13:  log likelihood = -4917.2554  (not concave)
Iteration 14:  log likelihood = -4917.2542  (not concave)
Iteration 15:  log likelihood = -4917.2531  (not concave)
Iteration 16:  log likelihood =  -4917.252  (not concave)
Iteration 17:  log likelihood = -4917.2511  (not concave)
Iteration 18:  log likelihood = -4917.2502  (not concave)
Iteration 19:  log likelihood = -4917.2493  (not concave)
Iteration 20:  log likelihood = -4917.2485  (not concave)
convergence not achieved

Conditional fixed-effects logistic regression        Number of obs    = 13,872
Group variable: pid                                  Number of groups =  2,474

Obs per group:
min =      2
avg =    5.6
max =     10

LR chi2(34)      = 196.67
Log likelihood = -4917.2485                          Prob > chi2      = 0.0000


resigning  Coefficient  Std. err.      z    P>z     [95% conf. interval]

insecurity 
L1.    .1586778   .0395872     4.01   0.000     .0810883    .2362673

ln_income 
L1.   -.0959634   .1089586    -0.88   0.378    -.3095183    .1175914

region 
2    -.0029459   .6049219    -0.00   0.996    -1.188571    1.182679
3     .0213726   .8443094     0.03   0.980    -1.633444    1.676189
4     54.71097          .        .       .            .           .
5     -1.05323   .7851114    -1.34   0.180     -2.59202    .4855604
6    -.3901004   .8363038    -0.47   0.641    -2.029226    1.249025
7     .6840851   1.003371     0.68   0.495    -1.282485    2.650655
8     .5695272   .8315001     0.68   0.493    -1.060183    2.199237
9     .0330805   .8980872     0.04   0.971    -1.727138    1.793299
10    -43.49452   1.72e+09    -0.00   1.000    -3.38e+09    3.38e+09
11     .9676775   .9933413     0.97   0.330    -.9792356    2.914591
12     .7399395   1.002769     0.74   0.461    -1.225452    2.705332
13     .8720612   1.059855     0.82   0.411    -1.205217    2.949339
14    -.1655239   1.044938    -0.16   0.874    -2.213564    1.882517
15    -1.174527   1.385044    -0.85   0.396    -3.889163    1.540109
16    -1.920376   1.317821    -1.46   0.145    -4.503258    .6625068

syear 
2011     .1142141   .0922802     1.24   0.216    -.0666517    .2950799
2012      .162089   .0917376     1.77   0.077    -.0177134    .3418914
2013     .2067589   .0895892     2.31   0.021     .0311674    .3823505
2014     .1426668   .0795742     1.79   0.073    -.0132957    .2986292
2015     .0924091   .0750384     1.23   0.218    -.0546635    .2394818
2016     .0959823   .0722217     1.33   0.184    -.0455696    .2375341
2017     .0659704   .0703078     0.94   0.348    -.0718303    .2037711
2018     .1146478   .0704689     1.63   0.104    -.0234688    .2527643
2019     .0564252          .        .       .            .           .

age 
L1.   -.1092868   .0493051    -2.22   0.027     -.205923   -.0126507

age2 
L1.    .0007596   .0005432     1.40   0.162    -.0003051    .0018242

L.married 
1    -.1836457   .1240138    -1.48   0.139    -.4267083    .0594169

L.health_status1 
2     .4764549   .2225177     2.14   0.032     .0403282    .9125817
3     .1984931   .2217544     0.90   0.371    -.2361375    .6331237
4     .1046584   .2238471     0.47   0.640    -.3340738    .5433906
5     .2330741   .2369465     0.98   0.325    -.2313325    .6974807

years_of_education 
L1.   -.0513078   .0984258    -0.52   0.602    -.2442188    .1416031

n_of_children 
L1.   -.1159357   .0600321    -1.93   0.053    -.2335965    .0017251

annual_working_hours 
L1.   -.0003312   .0000471    -7.03   0.000    -.0004236   -.0002388

. xtlogit resigning L.insecurity L.ln_income $yearsdummy i.region L.age L.age2 i.L.sex i.L.married    i.L.health_
> status1 L.years_of_education L.n_of_children L.annual_working_hours, fe iterate(20)
note: multiple positive outcomes within groups encountered.
note: 12,229 groups (50,752 obs) omitted because of all positive or
all negative outcomes.
note: 1L.sex omitted because of no within-group variance.

Iteration 0:   log likelihood = -4953.8719  
Iteration 1:   log likelihood = -4917.7094  
Iteration 2:   log likelihood = -4917.2589  
Iteration 3:   log likelihood = -4917.2287  
Iteration 4:   log likelihood = -4917.2222  
Iteration 5:   log likelihood = -4917.2207  
Iteration 6:   log likelihood = -4917.2204  
Iteration 7:   log likelihood = -4917.2203  
Iteration 8:   log likelihood = -4917.2203  

Conditional fixed-effects logistic regression        Number of obs    = 13,872
Group variable: pid                                  Number of groups =  2,474

Obs per group:
min =      2
avg =    5.6
max =     10

LR chi2(35)      = 196.73
Log likelihood = -4917.2203                          Prob > chi2      = 0.0000


resigning  Coefficient  Std. err.      z    P>z     [95% conf. interval]

insecurity 
L1.    .1595486   .0395919     4.03   0.000       .08195    .2371473

ln_income 
L1.   -.0939751   .1089648    -0.86   0.388    -.3075422     .119592

year11    .1067305   .0922694     1.16   0.247    -.0741142    .2875752
year12    .1484747   .0917286     1.62   0.106      -.03131    .3282595
year13    .1870052   .0895873     2.09   0.037     .0114174    .3625931
year14    .1159637   .0795739     1.46   0.145    -.0399984    .2719258
year15    .0599535    .075038     0.80   0.424    -.0871184    .2070253
year16    .0574416   .0722222     0.80   0.426    -.0841113    .1989945
year17    .0212388   .0703086     0.30   0.763    -.1165636    .1590412
year18    .0639982   .0704692     0.91   0.364     -.074119    .2021153

region 
2     -.010283   .6049746    -0.02   0.986    -1.196011    1.175445
3     .0200304   .8440641     0.02   0.981    -1.634305    1.674366
4     23.77858   26989.53     0.00   0.999    -52874.74     52922.3
5    -1.056672   .7848169    -1.35   0.178    -2.594885    .4815409
6    -.3918029    .836058    -0.47   0.639    -2.030447    1.246841
7     .6866278   1.003021     0.68   0.494    -1.279258    2.652514
8     .5670053   .8313347     0.68   0.495    -1.062381    2.196391
9     .0289339   .8978407     0.03   0.974    -1.730801    1.788669
10    -14.35951   810.0542    -0.02   0.986    -1602.037    1573.318
11      .966391   .9924808     0.97   0.330    -.9788356    2.911618
12     .7433985   1.002162     0.74   0.458    -1.220804    2.707601
13       .87058   1.059877     0.82   0.411    -1.206741    2.947901
14    -.1643945   1.044952    -0.16   0.875    -2.212463    1.883674
15    -1.177462   1.385052    -0.85   0.395    -3.892115     1.53719
16    -1.923164   1.317747    -1.46   0.144    -4.505901    .6595729

age 
L1.   -.1143711   .0492992    -2.32   0.020    -.2109957   -.0177464

age2 
L1.     .000883   .0005431     1.63   0.104    -.0001814    .0019474

L.sex 
1            0  (omitted)

L.married 
1    -.1807483   .1240086    -1.46   0.145    -.4238007    .0623041

L.health_status1 
2     .4649026   .2221624     2.09   0.036     .0294722    .9003329
3     .1864222   .2213913     0.84   0.400    -.2474967    .6203412
4     .0925622   .2234899     0.41   0.679    -.3454699    .5305943
5     .2207287   .2366089     0.93   0.351    -.2430162    .6844736

years_of_education 
L1.   -.0487996   .0984007    -0.50   0.620    -.2416614    .1440622

n_of_children 
L1.    -.112988   .0600387    -1.88   0.060    -.2306617    .0046858

annual_working_hours 
L1.   -.0003305   .0000471    -7.01   0.000    -.0004229   -.0002381

and with Age categories

. xtlogit resigning L.insecurity L.ln_income i.syear i.region i.L.age_cate i.L.sex i.L.married    i.L.health_stat
> us1 L.years_of_education L.n_of_children L.annual_working_hours, fe iterate(20)
note: multiple positive outcomes within groups encountered.
note: 12,207 groups (50,651 obs) omitted because of all positive or
all negative outcomes.
note: 1L.sex omitted because of no within-group variance.

Iteration 0:   log likelihood = -4954.8564  
Iteration 1:   log likelihood =    -4914.5  
Iteration 2:   log likelihood = -4914.0655  
Iteration 3:   log likelihood = -4914.0341  
Iteration 4:   log likelihood = -4914.0284  
Iteration 5:   log likelihood = -4914.0271  
Iteration 6:   log likelihood = -4914.0269  
Iteration 7:   log likelihood = -4914.0268  
Iteration 8:   log likelihood = -4914.0268  

Conditional fixed-effects logistic regression        Number of obs    = 13,866
Group variable: pid                                  Number of groups =  2,474

Obs per group:
min =      2
avg =    5.6
max =     10

LR chi2(37)      = 201.15
Log likelihood = -4914.0268                          Prob > chi2      = 0.0000


resigning  Coefficient  Std. err.      z    P>z     [95% conf. interval]

insecurity 
L1.    .1568622   .0395197     3.97   0.000      .079405    .2343195

ln_income 
L1.   -.0901518   .1090069    -0.83   0.408    -.3038015    .1234978

syear 
2011     .0686782   .0977131     0.70   0.482    -.1228359    .2601924
2012     .0736324   .1028235     0.72   0.474    -.1278979    .2751627
2013      .080782   .1058594     0.76   0.445    -.1266987    .2882627
2014    -.0216384   .1040958    -0.21   0.835    -.2256624    .1823856
2015    -.1144291   .1060272    -1.08   0.280    -.3222386    .0933803
2016    -.1529156   .1085844    -1.41   0.159    -.3657372     .059906
2017    -.2264816   .1120058    -2.02   0.043     -.446009   -.0069543
2018    -.2151943   .1162956    -1.85   0.064    -.4431294    .0127408
2019     -.319139   .1217926    -2.62   0.009     -.557848   -.0804299

region 
2    -.0053282   .6031277    -0.01   0.993    -1.187437     1.17678
3    -.0144088   .8435746    -0.02   0.986    -1.667785    1.638967
4      23.9593   29766.11     0.00   0.999    -58316.55    58364.47
5    -1.077494   .7862965    -1.37   0.171    -2.618607    .4636191
6    -.4071589   .8362864    -0.49   0.626     -2.04625    1.231932
7      .658063   1.002816     0.66   0.512     -1.30742    2.623546
8     .5285258   .8313712     0.64   0.525    -1.100932    2.157983
9     .0023187   .8976535     0.00   0.998     -1.75705    1.761687
10    -14.84499   1041.706    -0.01   0.989    -2056.552    2026.862
11     .9501312   .9967343     0.95   0.340    -1.003432    2.903694
12     .6816164   1.005483     0.68   0.498    -1.289094    2.652327
13     .8610184   1.057921     0.81   0.416    -1.212469    2.934506
14    -.2024885   1.044481    -0.19   0.846    -2.249633    1.844656
15    -1.178271   1.384005    -0.85   0.395     -3.89087    1.534328
16    -1.944648   1.316166    -1.48   0.140    -4.524285    .6349899

L.age_cate1 
2    -.3518934   .1504093    -2.34   0.019    -.6466902   -.0570965
3    -.3433212   .1950824    -1.76   0.078    -.7256756    .0390332
4    -.2346913   .2379139    -0.99   0.324     -.700994    .2316115

L.sex 
1            0  (omitted)

L.married 
1    -.1878148   .1241472    -1.51   0.130    -.4311388    .0555092

L.health_status1 
2     .4630734    .222156     2.08   0.037     .0276556    .8984911
3     .1842551   .2213972     0.83   0.405    -.2496754    .6181855
4     .0916305   .2234936     0.41   0.682     -.346409    .5296699
5     .2184561   .2366326     0.92   0.356    -.2453354    .6822476

years_of_education 
L1.   -.0569611   .0980777    -0.58   0.561    -.2491898    .1352676

n_of_children 
L1.   -.1095408   .0597734    -1.83   0.067    -.2266946     .007613

annual_working_hours 
L1.   -.0003309   .0000471    -7.02   0.000    -.0004233   -.0002385

Thank you for your help.

Alessandro

[Carlo Lazzaro]

Alessandro:
welcome to this forum-
I'm not sure if what follows cam be an answer to your issue, but creating a linear and a squared term for the same variable (instead of relying on -fvvarlist- notation) can increase convergence problem, as Stata consider them as two different variables.
What if you go:

L.age##L.age

[Alessandro Gallo]

Thank you very much for your answer, Carlo. I'll try it now.

[Alessandro Gallo]

I did try what you suggested and the convergence it's actually achieved with your command.

. xtlogit resignin L.insecurity L.ln_income i.region i.syear L.age##L.age i.L.married i.L.health_status1    L.ye
> ars_of_education L.n_of_children L.annual_working_hours, fe iterate(20)
note: multiple positive outcomes within groups encountered.
note: 12,229 groups (50,752 obs) omitted because of all positive or
all negative outcomes.
note: 75L.age omitted because of no within-group variance.
note: 76L.age omitted because of no within-group variance.
note: 77L.age omitted because of no within-group variance.
note: 78L.age omitted because of no within-group variance.
note: 79L.age omitted because of no within-group variance.
note: 80L.age omitted because of no within-group variance.
note: 81L.age omitted because of no within-group variance.
note: 89L.age omitted because of no within-group variance.
note: 90L.age omitted because of no within-group variance.

Iteration 0:   log likelihood = -4924.8066  (not concave)
Iteration 1:   log likelihood = -4886.3771  (not concave)
Iteration 2:   log likelihood = -4884.2786  (not concave)
Iteration 3:   log likelihood = -4881.7287  (not concave)
Iteration 4:   log likelihood = -4881.2378  (not concave)
Iteration 5:   log likelihood = -4880.9989  (not concave)
Iteration 6:   log likelihood = -4880.8407  
Iteration 7:   log likelihood = -4874.7921  (not concave)
Iteration 8:   log likelihood = -4874.7851  
Iteration 9:   log likelihood = -4874.7805  (not concave)
Iteration 10:  log likelihood = -4874.7805  (not concave)
Iteration 11:  log likelihood = -4874.7804  (not concave)
Iteration 12:  log likelihood = -4874.7804  (not concave)
Iteration 13:  log likelihood = -4874.7804  

Conditional fixed-effects logistic regression        Number of obs    = 13,872
Group variable: pid                                  Number of groups =  2,474

Obs per group:
min =      2
avg =    5.6
max =     10

LR chi2(33)      = 281.61
Log likelihood = -4874.7804                          Prob > chi2      = 0.0000


resignin  Coefficient  Std. err.      z    P>z     [95% conf. interval]

insecurity 
L1.    .1731396    .040145     4.31   0.000     .0944569    .2518223

ln_income 
L1.   -.0854216   .1100344    -0.78   0.438     -.301085    .1302417

region 
2    -.0858452   .6053189    -0.14   0.887    -1.272248    1.100558
3    -.0334152   .8441329    -0.04   0.968    -1.687885    1.621055
4     31.61253    1357427     0.00   1.000     -2660476     2660539
5    -1.116175   .7876348    -1.42   0.156    -2.659911    .4275609
6    -.4549247   .8382414    -0.54   0.587    -2.097848    1.187998
7     .6425368   1.008681     0.64   0.524    -1.334441    2.619515
8     .4972582   .8318461     0.60   0.550     -1.13313    2.127647
9    -.1007028   .8990822    -0.11   0.911    -1.862871    1.661466
10    -20.47941   18161.98    -0.00   0.999    -35617.31    35576.36
11     1.010452   .9993453     1.01   0.312    -.9482288    2.969133
12     .7041266   1.012967     0.70   0.487    -1.281253    2.689506
13     .8711515   1.074713     0.81   0.418    -1.235247     2.97755
14    -.2317229   1.052131    -0.22   0.826    -2.293862    1.830416
15     -1.25657   1.395447    -0.90   0.368    -3.991597    1.478457
16    -1.955408   1.317524    -1.48   0.138    -4.537707     .626891

syear 
2011    -.5215926   526128.3    -0.00   1.000     -1031193     1031192
2012      -1.1301    1052257    -0.00   1.000     -2062386     2062384
2013    -1.734734    1578385    -0.00   1.000     -3093579     3093576
2014    -2.445464    2104513    -0.00   1.000     -4124772     4124767
2015    -3.160096    2630641    -0.00   1.000     -5155965     5155959
2016    -3.816079    3156770    -0.00   1.000     -6187159     6187151
2017    -4.503509    3682898    -0.00   1.000     -7218352     7218343
2018    -5.099108    4209026    -0.00   1.000     -8249545     8249535
2019    -5.814061    4735154    -0.00   1.000     -9280738     9280726

L.age 
21    -14.22477     526129    -0.00   1.000     -1031208     1031180
22    -14.49808    1052257    -0.00   1.000     -2062400     2062371
23    -13.71678    1578385    -0.00   1.000     -3093592     3093565
24      -13.332    2104513    -0.00   1.000     -4124784     4124757
25    -12.33958    2630642    -0.00   1.000     -5155975     5155951
26    -11.83848    3156770    -0.00   1.000     -6187167     6187144
27    -11.80915    3682898    -0.00   1.000     -7218360     7218336
28    -11.07769    4209027    -0.00   1.000     -8249551     8249529
29    -10.72403    4735155    -0.00   1.000     -9280744     9280722
30    -10.38078    5261283    -0.00   1.000    -1.03e+07    1.03e+07
31    -9.610205    5787411    -0.00   1.000    -1.13e+07    1.13e+07
32    -9.019671    6313540    -0.00   1.000    -1.24e+07    1.24e+07
33     -8.62279    6839668    -0.00   1.000    -1.34e+07    1.34e+07
34    -7.813861    7365796    -0.00   1.000    -1.44e+07    1.44e+07
35    -7.273703    7891924    -0.00   1.000    -1.55e+07    1.55e+07
36    -6.592699    8418053    -0.00   1.000    -1.65e+07    1.65e+07
37    -6.139983    8944181    -0.00   1.000    -1.75e+07    1.75e+07
38     -5.62687    9470309    -0.00   1.000    -1.86e+07    1.86e+07
39    -4.694531    9996437    -0.00   1.000    -1.96e+07    1.96e+07
40    -4.111663   1.05e+07    -0.00   1.000    -2.06e+07    2.06e+07
41    -3.733726   1.10e+07    -0.00   1.000    -2.17e+07    2.17e+07
42     -3.02814   1.16e+07    -0.00   1.000    -2.27e+07    2.27e+07
43     -2.20537   1.21e+07    -0.00   1.000    -2.37e+07    2.37e+07
44    -1.873841   1.26e+07    -0.00   1.000    -2.47e+07    2.47e+07
45    -1.254301   1.32e+07    -0.00   1.000    -2.58e+07    2.58e+07
46    -.5209168   1.37e+07    -0.00   1.000    -2.68e+07    2.68e+07
47      .196691   1.42e+07     0.00   1.000    -2.78e+07    2.78e+07
48     1.107385   1.47e+07     0.00   1.000    -2.89e+07    2.89e+07
49     1.631821   1.53e+07     0.00   1.000    -2.99e+07    2.99e+07
50     2.221574   1.58e+07     0.00   1.000    -3.09e+07    3.09e+07
51     2.888617   1.63e+07     0.00   1.000    -3.20e+07    3.20e+07
52     3.345772   1.68e+07     0.00   1.000    -3.30e+07    3.30e+07
53     4.241327   1.74e+07     0.00   1.000    -3.40e+07    3.40e+07
54     4.952747   1.79e+07     0.00   1.000    -3.51e+07    3.51e+07
55     5.490245   1.84e+07     0.00   1.000    -3.61e+07    3.61e+07
56     5.798003   1.89e+07     0.00   1.000    -3.71e+07    3.71e+07
57     6.568023   1.95e+07     0.00   1.000    -3.82e+07    3.82e+07
58     6.887176   2.00e+07     0.00   1.000    -3.92e+07    3.92e+07
59     7.788285   2.05e+07     0.00   1.000    -4.02e+07    4.02e+07
60     8.065138   2.10e+07     0.00   1.000    -4.12e+07    4.12e+07
61     8.452867   2.16e+07     0.00   1.000    -4.23e+07    4.23e+07
62     9.279859   2.21e+07     0.00   1.000    -4.33e+07    4.33e+07
63     10.34993   2.26e+07     0.00   1.000    -4.43e+07    4.43e+07
64     10.68859   2.31e+07     0.00   1.000    -4.54e+07    4.54e+07
65     10.95062   2.37e+07     0.00   1.000    -4.64e+07    4.64e+07
66     11.74541   2.42e+07     0.00   1.000    -4.74e+07    4.74e+07
67     12.75738   2.47e+07     0.00   1.000    -4.85e+07    4.85e+07
68     12.43254   2.53e+07     0.00   1.000    -4.95e+07    4.95e+07
69    -6.040998   2.58e+07    -0.00   1.000    -5.05e+07    5.05e+07
70    -4.656019   2.63e+07    -0.00   1.000    -5.16e+07    5.16e+07
71    -4.370693   2.68e+07    -0.00   1.000    -5.26e+07    5.26e+07
72    -3.712264   2.74e+07    -0.00   1.000    -5.36e+07    5.36e+07
73    -3.105545   2.79e+07    -0.00   1.000    -5.47e+07    5.47e+07
74    -2.422734   2.84e+07    -0.00   1.000    -5.57e+07    5.57e+07
75            0  (empty)
76            0  (empty)
77            0  (empty)
78            0  (empty)
79            0  (empty)
80            0  (empty)
81            0  (empty)
89            0  (empty)
90            0  (empty)

L.married 
1    -.1846463   .1251609    -1.48   0.140    -.4299571    .0606645

L.health_status1 
2      .454165   .2239479     2.03   0.043     .0152352    .8930949
3     .1718108   .2232293     0.77   0.442    -.2657106    .6093322
4     .0728824   .2252964     0.32   0.746    -.3686905    .5144553
5      .212181   .2386899     0.89   0.374    -.2556425    .6800046

years_of_education 
L1.   -.0143068   .0993486    -0.14   0.885    -.2090264    .1804128

n_of_children 
L1.      -.0754   .0623098    -1.21   0.226    -.1975249    .0467249

annual_working_hours 
L1.   -.0003315   .0000475    -6.97   0.000    -.0004246   -.0002383

But what do I technically ask STATA when I type L.age##L.age (sorry I'm quite new to the software)?

Thank you for your help.

Kind regards,

Alessandro

[Carlo Lazzaro]

Alessandro:
you're basically asking an interaction between (lagged) -age- and itself.
This code tells Stata that you want both the linear and the squared terms for the very same variabe -age-.
This is very helpful, as, over and above making your regression easier, this way you have a priority lane to exploit the wonderful capabilities of -margisn. and -marginsplot- commands.

[Alessandro Gallo]

Ok, I get it. Thank you Carlo for your help.

Kind regards,

Alessandro

[Alessandro Gallo]

Hi Carlo,

I actually realised that with the code that you suggested I do not find the squared age effect, on the contrary, I think I might find the effect of Age if Age is considered as a categorical variable with 54 categories. While if I run the regression with the code:

c.L.age##c.L.age

I get the squared term. With this new code, STATA still cannot find convergence. So I don't know if the convergence problem was caused by what you suggested in #3

Here is the code:

 xtlogit jobchange L.insecurity L.ln_income i.region i.syear c.L.age##c.L.age i.L.married i.L.health_status1 L.yea
> rs_of_education L.n_of_children L.annual_working_hours if resignin1 == 0, fe iterate(40)
note: multiple positive outcomes within groups encountered.
note: 12,623 groups (55,604 obs) omitted because of all positive or
      all negative outcomes.

Iteration 0:   log likelihood = -5000.2675  (not concave)
Iteration 1:   log likelihood = -4970.1339  (not concave)
Iteration 2:   log likelihood = -4965.8388  (not concave)
Iteration 3:   log likelihood = -4964.7925  (not concave)
Iteration 4:   log likelihood = -4964.2802  (not concave)
Iteration 5:   log likelihood = -4964.0256  (not concave)
Iteration 6:   log likelihood = -4963.7475  (not concave)
Iteration 7:   log likelihood = -4963.3296  (not concave)
Iteration 8:   log likelihood = -4963.1443  (not concave)
Iteration 9:   log likelihood =  -4963.002  (not concave)
Iteration 10:  log likelihood = -4962.8849  (not concave)
Iteration 11:  log likelihood = -4962.7828  (not concave)
Iteration 12:  log likelihood = -4962.6791  (not concave)
Iteration 13:  log likelihood =  -4962.601  (not concave)
Iteration 14:  log likelihood = -4962.5308  (not concave)
Iteration 15:  log likelihood = -4962.4606  (not concave)
Iteration 16:  log likelihood = -4962.4027  (not concave)
Iteration 17:  log likelihood = -4962.3511  (not concave)
Iteration 18:  log likelihood = -4962.3021  (not concave)
Iteration 19:  log likelihood = -4962.2592  (not concave)
Iteration 20:  log likelihood = -4962.2206  (not concave)
Iteration 21:  log likelihood = -4962.1851  (not concave)
Iteration 22:  log likelihood = -4962.1531  (not concave)
Iteration 23:  log likelihood = -4962.1242  (not concave)
Iteration 24:  log likelihood = -4962.0979  (not concave)
Iteration 25:  log likelihood = -4962.0741  (not concave)
Iteration 26:  log likelihood = -4962.0525  (not concave)
Iteration 27:  log likelihood =  -4962.033  (not concave)
Iteration 28:  log likelihood = -4962.0153  (not concave)
Iteration 29:  log likelihood = -4961.9992  (not concave)
Iteration 30:  log likelihood = -4961.9923  (not concave)
Iteration 31:  log likelihood = -4961.9872  (not concave)
Iteration 32:  log likelihood = -4961.9822  (not concave)
Iteration 33:  log likelihood = -4961.9374  (not concave)
Iteration 34:  log likelihood =   -4961.89  (not concave)
Iteration 35:  log likelihood = -4961.8844  (not concave)
Iteration 36:  log likelihood =  -4961.883  (not concave)
Iteration 37:  log likelihood = -4961.8819  (not concave)
Iteration 38:  log likelihood = -4961.8808  (not concave)
Iteration 39:  log likelihood = -4961.8797  (not concave)
Iteration 40:  log likelihood = -4961.8787  (not concave)
convergence not achieved

Conditional fixed-effects logistic regression        Number of obs    = 14,507
Group variable: pid                                  Number of groups =  2,472

                                                     Obs per group:
                                                                  min =      2
                                                                  avg =    5.9
                                                                  max =     11

                                                     LR chi2(35)      = 266.06
Log likelihood = -4961.8787                          Prob > chi2      = 0.0000

--------------------------------------------------------------------------------------
           jobchange | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------------+----------------------------------------------------------------
          insecurity |
                 L1. |   .1686361   .0398847     4.23   0.000     .0904635    .2468086
                     |
           ln_income |
                 L1. |   -.124592   .1075287    -1.16   0.247    -.3353444    .0861603
                     |
              region |
                  2  |   .2909467   .5697053     0.51   0.610     -.825655    1.407549
                  3  |  -.0096278   .7890984    -0.01   0.990    -1.556232    1.536977
                  4  |   78.52162          .        .       .            .           .
                  5  |  -.5981331    .738387    -0.81   0.418    -2.045345    .8490788
                  6  |  -.8611125    .791931    -1.09   0.277    -2.413269    .6910437
                  7  |  -.1669472   .9298269    -0.18   0.858    -1.989374     1.65548
                  8  |   .0864494   .7810748     0.11   0.912    -1.444429    1.617328
                  9  |  -.4170926   .8429763    -0.49   0.621    -2.069296    1.235111
                 10  |    .617145   1.835276     0.34   0.737     -2.97993     4.21422
                 11  |   .6460224   .9387501     0.69   0.491    -1.193894    2.485939
                 12  |   .8378722   .9435949     0.89   0.375     -1.01154    2.687284
                 13  |   1.891317   1.061946     1.78   0.075    -.1900594    3.972693
                 14  |  -.6767784   .9460082    -0.72   0.474     -2.53092    1.177364
                 15  |  -1.110674   1.415976    -0.78   0.433    -3.885935    1.664588
                 16  |  -1.683184    1.10992    -1.52   0.129    -3.858587    .4922199
                     |
               syear |
               2011  |   .1299577    .102722     1.27   0.206    -.0713738    .3312892
               2012  |   .1784093   .1006204     1.77   0.076    -.0188031    .3756217
               2013  |   .2792189   .0968137     2.88   0.004     .0894675    .4689704
               2014  |   .1314178   .0879603     1.49   0.135    -.0409812    .3038168
               2015  |   .1052914    .082946     1.27   0.204    -.0572797    .2678626
               2016  |   .1319805   .0790316     1.67   0.095    -.0229186    .2868795
               2017  |   .1080491   .0771426     1.40   0.161    -.0431476    .2592457
               2018  |   .1030712   .0777513     1.33   0.185    -.0493186    .2554609
               2019  |   .0092368    .079064     0.12   0.907    -.1457258    .1641994
               2020  |  -.2364942          .        .       .            .           .
                     |
                 age |
                 L1. |  -.1721143   .0467997    -3.68   0.000    -.2638401   -.0803885
                     |
       cL.age#cL.age |   .0015522   .0005174     3.00   0.003     .0005382    .0025662
                     |
           L.married |
                  1  |  -.2069814   .1216313    -1.70   0.089    -.4453744    .0314116
                     |
    L.health_status1 |
                  2  |   .3088299   .2329175     1.33   0.185    -.1476799    .7653398
                  3  |   .0511977   .2319515     0.22   0.825    -.4034189    .5058142
                  4  |  -.0551506   .2338465    -0.24   0.814    -.5134812    .4031801
                  5  |   .0653898   .2455752     0.27   0.790    -.4159287    .5467082
                     |
  years_of_education |
                 L1. |   -.021139   .0898088    -0.24   0.814     -.197161     .154883
                     |
       n_of_children |
                 L1. |  -.0662271   .0584493    -1.13   0.257    -.1807856    .0483314
                     |
annual_working_hours |
                 L1. |  -.0003555   .0000466    -7.64   0.000    -.0004468   -.0002643
--------------------------------------------------------------------------------------

Thank you again in advance for your help.

[Carlo Lazzaro]

Alesandro:
the following

note: multiple positive outcomes within groups encountered.
note: 12,623 groups (55,604 obs) omitted because of all positive or
all negative outcomes.

might have caused convergence problem.
Categorizing a continous predictor like -Age- does not make much sense (see, if interested,

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.462.859&rep=rep1&type=pdf

).
The usual recipe when convergence is not achieved is to start it all over again, adding one predictor at a time and see when the MLE starts to gasp.