Dear All,
I have an individual-by-week panel for 52 weeks. I want to examine the effect of a variable 'tot' on probability of death. My data looks as follows:

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input long case_number byte week float(death tot male) byte(race age1639 age40plus eduhs edulcol educol edupg edumiss) float(ever_op ever_od ever_booked ever_total_ed)
100064  1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  2 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  3 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  4 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  5 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  6 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  7 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  8 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064  9 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 10 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 11 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 12 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 13 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 14 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 15 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 16 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 17 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 18 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 19 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 20 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 21 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 22 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 23 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 24 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 25 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 26 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 27 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 28 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 29 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 30 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 31 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 32 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 33 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 34 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 35 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 36 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 37 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 38 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 39 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 40 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 41 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 42 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 43 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 44 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 45 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 46 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 47 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 48 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 49 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 50 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 51 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100064 52 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0
100076  1 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  2 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  3 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  4 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  5 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  6 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  7 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  8 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076  9 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 10 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 11 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 12 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 13 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 14 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 15 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 16 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 17 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 18 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 19 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 20 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 21 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 22 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 23 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 24 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 25 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 26 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 27 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 28 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 29 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 30 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 31 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 32 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 33 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 34 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 35 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 36 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 37 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 38 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 39 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 40 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 41 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 42 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 43 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 44 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 45 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 46 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 47 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
100076 48 0 0 1 2 0 1 1 0 0 0 0 0 0 0 0
end

My key independent variable 'tot' ranges from 0-38, however its skewed.

Code:
. tab tot, miss

        tot |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |     82,690       68.45       68.45
          1 |     18,441       15.27       83.72
          2 |      8,355        6.92       90.64
          3 |      4,211        3.49       94.12
          4 |      2,360        1.95       96.08
          5 |      1,493        1.24       97.31
          6 |        899        0.74       98.06
          7 |        644        0.53       98.59
          8 |        477        0.39       98.99
          9 |        200        0.17       99.15
         10 |        183        0.15       99.30
         11 |        140        0.12       99.42
         12 |        126        0.10       99.52
         13 |        125        0.10       99.63
         14 |         90        0.07       99.70
         15 |         74        0.06       99.76
         16 |        111        0.09       99.85
         17 |         27        0.02       99.88
         18 |         29        0.02       99.90
         19 |         28        0.02       99.92
         20 |         45        0.04       99.96
         21 |         10        0.01       99.97
         22 |          6        0.00       99.97
         23 |         11        0.01       99.98
         24 |          3        0.00       99.99
         25 |          1        0.00       99.99
         26 |          1        0.00       99.99
         27 |          1        0.00       99.99
         28 |          1        0.00       99.99
         29 |          1        0.00       99.99
         30 |          1        0.00       99.99
         31 |          1        0.00       99.99
         32 |          2        0.00       99.99
         33 |          1        0.00       99.99
         34 |          2        0.00      100.00
         35 |          1        0.00      100.00
         36 |          3        0.00      100.00
         37 |          1        0.00      100.00
         38 |          1        0.00      100.00
------------+-----------------------------------
      Total |    120,796      100.00
To examine the effect of 'tot' on the probability of death I estimate the following regression:

Code:
. logit death tot  $covariates c.yw, or vce(cluster case_number) 

Iteration 0:   log pseudolikelihood = -11479.258  
Iteration 1:   log pseudolikelihood =  -11214.26  
Iteration 2:   log pseudolikelihood = -11183.852  
Iteration 3:   log pseudolikelihood = -11183.824  
Iteration 4:   log pseudolikelihood = -11183.824  

Logistic regression                             Number of obs     =    120,796
                                                Wald chi2(11)     =     727.94
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -11183.824               Pseudo R2         =     0.0257

                        (Std. Err. adjusted for 2,323 clusters in case_number)
------------------------------------------------------------------------------
             |               Robust
       death | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         tot |    1.16571    .017594    10.16   0.000     1.131731    1.200708
        male |   1.071387   .0338684     2.18   0.029     1.007021    1.139868
             |
        race |
          2  |   .9537488    .033283    -1.36   0.175     .8906962    1.021265
          3  |   1.081874   .0478604     1.78   0.075     .9920214    1.179866
          4  |   .9813072   .0397271    -0.47   0.641     .9064525    1.062343
             |
     age1639 |   1.005282   .0269937     0.20   0.844     .9537432    1.059605
       eduhs |   .9189303   .0226669    -3.43   0.001     .8755607    .9644481
      educol |   1.107214   .0361908     3.12   0.002     1.038505    1.180467
       edupg |   1.143021   .1018002     1.50   0.133     .9599403     1.36102
     edumiss |   .8451781   .0305153    -4.66   0.000     .7874363     .907154
          yw |   1.001862   .0001051    17.74   0.000     1.001656    1.002068
       _cons |   .0000819   .0000232   -33.27   0.000     .0000471    .0001426
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.
Thereafter, I am not sure which is the correct version of margins command I should follow up with because they give very different shapes.


OPTION 1: Monotonically increasing.

Code:
 margins, dydx(tot) at(tot=(0(2)38))

Average marginal effects                        Number of obs     =    120,796
Model VCE    : Robust

Expression   : Pr(death), predict()
dy/dx w.r.t. : tot

1._at        : tot             =           0

2._at        : tot             =           2

3._at        : tot             =           4

4._at        : tot             =           6

5._at        : tot             =           8

6._at        : tot             =          10

7._at        : tot             =          12

8._at        : tot             =          14

9._at        : tot             =          16

10._at       : tot             =          18

11._at       : tot             =          20

12._at       : tot             =          22

13._at       : tot             =          24

14._at       : tot             =          26

15._at       : tot             =          28

16._at       : tot             =          30

17._at       : tot             =          32

18._at       : tot             =          34

19._at       : tot             =          36

20._at       : tot             =          38

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
tot          |
         _at |
          1  |    .002435   .0002032    11.98   0.000     .0020366    .0028333
          2  |   .0032689   .0003674     8.90   0.000     .0025489    .0039889
          3  |   .0043699   .0006137     7.12   0.000     .0031671    .0055727
          4  |   .0058089   .0009711     5.98   0.000     .0039056    .0077121
          5  |   .0076643   .0014711     5.21   0.000      .004781    .0105475
          6  |   .0100136   .0021417     4.68   0.000     .0058159    .0142113
          7  |   .0129175   .0029953     4.31   0.000     .0070468    .0187882
          8  |   .0163934   .0040091     4.09   0.000     .0085357    .0242512
          9  |   .0203815   .0051016     4.00   0.000     .0103826    .0303804
         10  |   .0247062   .0061126     4.04   0.000     .0127257    .0366866
         11  |   .0290524   .0068067     4.27   0.000     .0157116    .0423932
         12  |   .0329767    .006917     4.77   0.000     .0194196    .0465338
         13  |   .0359731   .0062361     5.77   0.000     .0237506    .0481955
         14  |     .03759   .0047208     7.96   0.000     .0283374    .0468427
         15  |    .037562   .0025534    14.71   0.000     .0325575    .0425665
         16  |   .0358954   .0001211   296.34   0.000      .035658    .0361329
         17  |   .0328661   .0022006    14.93   0.000     .0285529    .0371792
         18  |   .0289285   .0040057     7.22   0.000     .0210776    .0367795
         19  |   .0245856   .0051431     4.78   0.000     .0145053     .034666
         20  |   .0202747   .0056198     3.61   0.000       .00926    .0312893
------------------------------------------------------------------------------

. marginsplot, recast(line) recastci(rarea) ciopt(lcolor(navy) fcolor(ebblue) color(%20)) plot1opts(lcolor(navy) fcolor(ebblue%
> 35))
:

OPTION 2: Here the line is not monotonically increasing.

Code:
. margins, at(tot=(0(2)38)) post

Predictive margins                              Number of obs     =    120,796
Model VCE    : Robust

Expression   : Pr(death), predict()

1._at        : tot             =           0

2._at        : tot             =           2

3._at        : tot             =           4

4._at        : tot             =           6

5._at        : tot             =           8

6._at        : tot             =          10

7._at        : tot             =          12

8._at        : tot             =          14

9._at        : tot             =          16

10._at       : tot             =          18

11._at       : tot             =          20

12._at       : tot             =          22

13._at       : tot             =          24

14._at       : tot             =          26

15._at       : tot             =          28

16._at       : tot             =          30

17._at       : tot             =          32

18._at       : tot             =          34

19._at       : tot             =          36

20._at       : tot             =          38

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .0161552   .0002804    57.61   0.000     .0156055    .0167048
          2  |   .0218199   .0003474    62.81   0.000      .021139    .0225007
          3  |   .0294085   .0012881    22.83   0.000     .0268839    .0319331
          4  |   .0395245   .0028461    13.89   0.000     .0339462    .0451028
          5  |   .0529216   .0052592    10.06   0.000     .0426138    .0632294
          6  |   .0705113     .00884     7.98   0.000     .0531851    .0878374
          7  |   .0933467   .0139457     6.69   0.000     .0660136    .1206798
          8  |   .1225643    .020927     5.86   0.000     .0815481    .1635805
          9  |   .1592645   .0300344     5.30   0.000     .1003981    .2181308
         10  |   .2043179   .0412789     4.95   0.000     .1234126    .2852231
         11  |   .2581065   .0542725     4.76   0.000     .1517342    .3644787
         12  |   .3202477   .0681134     4.70   0.000     .1867479    .4537475
         13  |   .3893935   .0814074     4.78   0.000      .229838     .548949
         14  |   .4632161   .0924939     5.01   0.000     .2819313    .6445009
         15  |   .5386507   .0998485     5.39   0.000     .3429511    .7343502
         16  |   .6123655   .1025131     5.97   0.000     .4114435    .8132875
         17  |   .6813198   .1003565     6.79   0.000     .4846246     .878015
         18  |   .7432234   .0940483     7.90   0.000     .5588921    .9275546
         19  |   .7967653   .0847843     9.40   0.000     .6305911    .9629395
         20  |   .8415902   .0739196    11.39   0.000     .6967105    .9864699
------------------------------------------------------------------------------

. marginsplot, recast(line) recastci(rarea) ciopt(lcolor(navy) fcolor(ebblue) color(%20)) plot1opts(lcolor(navy) fcolor(ebblue%
> 35))
Which one is correct?
Many thanks for your help.
Sumedha.