Binary Logit Regression - Interpreting Results

[Guest]

Hi all,

I am using panel data and I am trying to run a logistic regression with a binary dependent variable. The dependent variable is a dummy variable taking values 1 if respondent is a heavy cash user and 0 if they are not. I am trying to estimate the probability that changes in age, income and education produce certain outcome. (not sure if a worded that correctly)

I used the following code and attach the data example:

logit cashusage age incometh i.educat male credit rating holdings if sample==1, robust cluster(newID)

logistic cashusage age incometh i.educat male credit rating holdings if sample==1, robust cluster(newID)

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(newID year cashusage) double age float(incometh educat male) double credit float rating double holdings float sample
 1 2015 0 31 112.5 4 1 1 20 108.33333333333341 1
 1 2016 1 32 112.5 4 1 1 21                 20 1
 1 2017 0 34 112.5 4 1 1 24  969.6428580000008 1
 2 2015 0 66  27.5 4 0 1 21  300.0000000000001 1
 2 2016 0 67  17.5 4 0 1 22 180.00000000000006 1
 2 2017 0 68  17.5 4 0 1 23                280 1
 3 2016 0 41 112.5 3 1 1 29                  0 1
 3 2017 1 42 112.5 3 1 1 25                 80 1
 4 2015 0 25  32.5 2 1 0 25               82.5 1
 4 2016 0 26  37.5 2 1 0 26 11.666666666666664 1
 4 2017 0 27  37.5 2 1 1 24  973.9285715999991 1
 5 2015 1 53  37.5 3 0 1 21 130.44642870000004 1
 5 2016 0 55  32.5 3 0 1 23  80.00000000000001 1
 5 2017 1 56  22.5 3 0 1 22  60.00000000000001 1
 6 2015 0 26    55 4 0 1 20                 80 1
 6 2016 0 28    55 4 0 1 20                 20 1
 7 2015 0 83 112.5 3 1 1 22 1304.4642869999998 1
 7 2016 0 84 112.5 3 1 1 18                600 1
 7 2017 0 85 112.5 3 1 1 20                300 0
 8 2015 0 38 112.5 3 1 1 14  83.33333333333327 1
 8 2016 0 40 162.5 3 1 1 17  85.73735572900041 1
 8 2017 0 41 162.5 3 1 1 15 199.99999999999994 1
 9 2015 1 57  22.5 2 0 1 29                 80 1
 9 2016 0 58  22.5 2 0 1 28 200.00000000000014 1
 9 2017 1 59  22.5 2 0 1 29 13.333333333333336 1
10 2015 0 57 162.5 4 1 1 22  869.6428579999998 1
10 2016 0 58    55 4 1 1 23  710.3417382269064 1
10 2017 0 59    45 4 1 1 21  869.6428579999998 1
11 2015 1 44  87.5 3 1 1 23 434.82142900000036 1
11 2016 1 46  87.5 3 1 1 23 434.82142900000036 1
11 2017 1 47  87.5 3 1 1 23 500.00000000000045 1
12 2015 0 54 162.5 3 1 1 21  150.0000000000001 1
12 2016 0 56 162.5 3 1 1 22                 40 1
12 2017 0 57 162.5 3 1 1 24  60.00000000000001 1
13 2015 0 64  17.5 3 0 1 16 100.00000000000007 1
13 2016 0 66  17.5 3 0 1 22   708.333333333333 1
13 2017 0 67 11.25 3 0 1 19                300 1
14 2015 1 48  6.25 3 0 0 24        2174.107145 1
14 2016 1 49  8.75 3 0 0 30 1779.2857159999999 0
14 2017 1 50  8.75 3 0 0 24  521.7857148000004 1
15 2015 0 54 112.5 3 0 1 24  257.4107145000001 1
15 2017 1 57 112.5 3 0 1 16                  . 0
16 2015 0 56 162.5 3 1 1 19 200.00000000000014 1
16 2016 0 58 162.5 3 1 1 22 100.00000000000006 1
16 2017 0 58 162.5 3 1 1 20 100.00000000000007 1
17 2015 0 53  67.5 2 1 1 25 373.92857160000017 1
17 2016 1 55  67.5 2 1 0 19 240.00000000000014 1
18 2015 0 47 162.5 3 0 1 19  33.33333333333334 1
18 2017 0 50 162.5 3 0 1 14 100.00000000000007 1
19 2015 0 49  67.5 4 1 1 21 23.333333333333336 1
19 2016 0 51  67.5 4 1 1 19                 40 1
19 2017 0 52  67.5 4 1 1 26                 80 1
20 2015 0 62  87.5 2 1 1 24  280.8928574000001 1
20 2016 0 64 112.5 2 1 1 24 180.00000000000006 1
20 2017 0 64 112.5 2 1 1 23 146.96428580000003 1
21 2015 0 64  8.75 3 0 1 16 173.92857160000003 1
21 2016 1 65  8.75 3 0 1 23  95.29761913333337 1
21 2017 1 66  8.75 3 0 1 17                120 1
22 2016 1 50  32.5 2 1 1 25  782.6785722000002 1
22 2017 1 51  32.5 2 1 1 22  360.0000000000001 1
23 2015 0 46 162.5 4 1 1 19                 20 1
23 2017 0 49 162.5 4 1 1 20                 80 1
24 2015 0 44  87.5 3 1 1 20               1600 1
24 2016 1 45 112.5 3 1 1 20 120.00000000000001 1
24 2017 0 46 112.5 3 1 1 16 100.00000000000007 1
25 2015 0 28   2.5 4 0 1 16                260 1
25 2016 0 29  17.5 4 0 1 21                 80 1
25 2017 0 30  27.5 4 0 1 17 46.666666666666664 1
26 2015 0 30    45 4 0 1 17 100.00000000000007 1
26 2016 0 32    45 4 0 1 25                 60 1
26 2017 0 32    45 4 0 1 23 100.00000000000007 1
27 2015 0 52  67.5 4 1 1 20 200.00000000000014 1
27 2016 0 52  67.5 4 1 1 21  360.0000000000003 1
27 2017 0 53  67.5 4 1 1 19  340.0000000000003 1
28 2015 0 46 162.5 3 1 1 17  554.8214290000002 1
28 2016 0 47 112.5 3 1 1 22 180.00000000000006 1
28 2017 1 48 112.5 3 1 1 24 120.00000000000001 1
29 2015 0 31  67.5 3 1 1 20                 20 1
29 2016 0 33  67.5 3 1 1 22                160 1
29 2017 0 34  67.5 3 1 1 20                 40 1
30 2015 1 56  67.5 2 1 0 29 3892.8854616688204 1
30 2016 0 58  67.5 2 1 0 19 126.96428580000003 1
30 2017 0 59  87.5 2 1 0 19 213.92857160000003 1
31 2015 1 58  32.5 2 1 0 25 195.66964305000005 1
31 2016 1 60  32.5 2 1 0 22 200.00000000000014 1
31 2017 1 61  32.5 2 1 0 22 200.00000000000003 1
32 2015 0 30 112.5 3 1 1 21  33.33333333333334 1
32 2016 0 32 112.5 3 1 1 21 25.000000000000018 1
32 2017 0 33 112.5 3 1 1 22   41.6666666666667 1
33 2015 1 59  67.5 2 1 0 15 1739.2857159999999 1
33 2016 1 61  67.5 2 1 0 23  521.7857148000002 1
34 2015 1 69  8.75 1 1 .  .                  . 0
34 2016 1 69  8.75 1 1 0 12 130.44642870000007 1
34 2017 1 71  8.75 1 1 0 17 173.92857160000003 1
35 2015 0 53  87.5 3 1 1 25  53.33333333333333 1
35 2016 0 54  67.5 3 1 0 21                 20 1
35 2017 0 55  87.5 3 1 0 26  33.33333333333333 1
36 2015 1 37 13.75 3 0 0 23 180.00000000000003 1
36 2016 0 39  8.75 3 0 0 23 213.92857160000003 1
36 2017 0 40 11.25 3 0 0 21 173.92857160000003 1
end
label values newID newID
label def newID 1 "140100007", modify
label def newID 2 "140100010", modify
label def newID 3 "140100035", modify
label def newID 4 "140100038", modify
label def newID 5 "140100047", modify
label def newID 6 "140100048", modify
label def newID 7 "140100055", modify
label def newID 8 "140100072", modify
label def newID 9 "140100081", modify
label def newID 10 "140100108", modify
label def newID 11 "140100116", modify
label def newID 12 "140100125", modify
label def newID 13 "140100143", modify
label def newID 14 "140100144", modify
label def newID 15 "140100160", modify
label def newID 16 "140100168", modify
label def newID 17 "140100175", modify
label def newID 18 "140100179", modify
label def newID 19 "140100183", modify
label def newID 20 "140100236", modify
label def newID 21 "140100244", modify
label def newID 22 "140100288", modify
label def newID 23 "140100295", modify
label def newID 24 "140100299", modify
label def newID 25 "140100300", modify
label def newID 26 "140100307", modify
label def newID 27 "140100310", modify
label def newID 28 "140100317", modify
label def newID 29 "140100324", modify
label def newID 30 "140100329", modify
label def newID 31 "140100333", modify
label def newID 32 "140100335", modify
label def newID 33 "140100341", modify
label def newID 34 "140100346", modify
label def newID 35 "140100378", modify
label def newID 36 "140100414", modify
label values educat educat_label
label def educat_label 1 "no diploma", modify
label def educat_label 2 "high school", modify
label def educat_label 3 "graduate", modify
label def educat_label 4 "post graduate", modify
label values male male_label
label def male_label 0 "female", modify
label def male_label 1 "male", modify
label values credit credit_label
label def credit_label 0 "no credit card", modify
label def credit_label 1 "credit card owner", modify

Questions:

1. What do the iterations mean when I run this regression?

2. How can I correctly interpret the coefficient on age income and i.educat?

As far as I understand:

• If the odds ratio for age is 1.01 then “A one year increase in age is associated with a increase odds of being a heavy cash user by a factor of 1.01”
• If the odds ratio for high school in i.educat then "The odds of being a heavy cash user is 9.79 times higher for those with a high school diploma those with no diploma
• If the odds ratio for income is 0.97 then “A one thousand dollar increase in income is associated with decreased odds of being a heavy cash user by a factor of 0.97”

is the following reasoning correct?

• I say “decreased odds” if the coefficient from the logit regression indicates a negative relationship. Although, i think I am getting confused as to when I should say “increased vs decreased odds”.
• I say “by a factor of X” if the odds ratio value is X

3. Why would certain variables be automatically omitted from this regression?

4. Should I be including i.year as I have done in OLS estimation?

I am only used to performing OLS estimation to I feel somewhat out of depth here. Any extra advice would be really useful. Thanks!

[Phil Bromiley]

You don't need to give us data with piles and piles of label definitions. This is not really relevant to the problem.

Regarding your questions:
1. This is a maximum likelihood estimator – it is searching around to find the estimates that best fit the model. In doing that searching Iran's and iterations which are stages of tentative parameters.
2. I personally find running logit with probabilities easier to interpret than odds ratios, and then I use the margin statement afterwards to get differences in predicted probabilities. Read the logit and logit post estimation and margins documentation.

[Guest]

Thanks very much Phil for your advice.

So, for example, if a coefficient is 1.90 for income does this mean that an increase in income increases the probability of being a heavy cash user by 90%?