Doubts on interpreting my glm coeffcients

[marcelo ribeiro]

Dear all,

I want to verify if I'm interpreting my glm model right. I have a dependent variable, in percentage, (the percentage of the country i population which gave money to charity in 2010, i=1,...,44) and independent variables also measured in percentages (e.g. percentage of the country i population that feels happy).

I used a glm model

You can see my dataset using:

dataex givingmoney Souci_humankind_much tolerance_at_home_mentioned Justifyied_cheat_tax_never Unemployed_should_take_any_job Do_you_consider_you_religious past_frequence_week_month q11_how_satisfied_with_life_very

input float(givingmoney Souci_humankind_much tolerance_at_home_mentioned Justifyied_cheat_tax_never Unemployed_should_take_any_job Do_you_consider_you_religious past_frequence_week_month q11_how_satisfied_with_life_very)

.27 11.83 55.74  48.2  59.5  90.8     9.48 34.97
.69 10.88 68.72 56.71 55.95 63.88     58.7  61.1
.06 17.43 66.87 62.26 33.04 88.71    31.55 28.28
 .4 10.31 82.24 40.25 53.95 57.79    67.22 63.86
.29 10.84 58.13 73.55 39.57 94.82    50.03  50.6
.18 12.15 65.21 68.11 55.15 61.15    11.35 30.47
.11 14.08 63.87 27.68 39.02 31.78    11.92 28.56
.26 10.97 70.21 58.16 43.72 83.61    75.09 53.11

I'm using the glm command:

glm givingmoney Souci_humankind_much tolerance_at_home_mentioned Justifyied_cheat_tax_never Unemployed_should_take_any_job Do_you_consider_you_religious past_frequence_week_month q11_how_satisfied_with_life_very ,  family(binomial) link(logit) robust

I verified my resid :

ovfplot

and

rvfplot2, yline(0)

and I want to interpret the effect of my independent variables:
I used

mfx

.

How do I interpret these figures? As I'm using a link(logit) it should be : one unit increase in my independent variable causes a exp(coefficient value) change (odds ratio) in the dependent variable. However,how a one unit change in a independent variable in % should be interpreted? a 1% increase in the independent variable causes exp(coefficient)% in the dependent variable?

Thank you

[Marcos Almeida]

It seems the DV is not in percentage, for it is a proportion. But the IVs are shown in percentages. You didn’t provide the output, but I gather the interpretation would probably take an increase in 1% of the IV to be associated with a change in # percentage points of the DV. Margins and marginsplot are helpful as well.

[marcelo ribeiro]

glm givingmoney Souci_humankind_much tolerance_at_home_mentioned Justifyied_adultery Unemployed_should_t
> ake_any_job Do_you_consider_you_religious past_frequence_week_month why_people_in_need_unlucky q8_5 q11_
> how_satisfied_with_life_very ,  family(binomial) link(logit) robust
note: givingmoney has noninteger values

Iteration 0:   log pseudolikelihood =  -16.66969
Iteration 1:   log pseudolikelihood = -16.554162
Iteration 2:   log pseudolikelihood = -16.554126
Iteration 3:   log pseudolikelihood = -16.554126

Generalized linear models                          No. of obs      =        44
Optimization     : ML                              Residual df     =        34
                                                   Scale parameter =         1
Deviance         =  2.122978712                    (1/df) Deviance =  .0624406
Pearson          =  2.145369357                    (1/df) Pearson  =  .0630991

Variance function: V(u) = u*(1-u/1)                [Binomial]
Link function    : g(u) = ln(u/(1-u))              [Logit]

                                                   AIC             =  1.207006
Log pseudolikelihood = -16.55412626                BIC             = -126.5395

--------------------------------------------------------------------------------------------------
                                 |               Robust
                     givingmoney |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------------+----------------------------------------------------------------
            Souci_humankind_much |   .0006955   .0096602     0.07   0.943    -.0182381    .0196292
     tolerance_at_home_mentioned |    .000144   .0081629     0.02   0.986    -.0158549     .016143
             Justifyied_adultery |   .0167571   .0067305     2.49   0.013     .0035655    .0299487
  Unemployed_should_take_any_job |   .0283718   .0097493     2.91   0.004     .0092634    .0474801
   Do_you_consider_you_religious |  -.0138382   .0060726    -2.28   0.023    -.0257402   -.0019362
       past_frequence_week_month |    .013365   .0041612     3.21   0.001     .0052093    .0215208
      why_people_in_need_unlucky |  -.0125862   .0180596    -0.70   0.486    -.0479824      .02281
                            q8_5 |  -.0407581   .0213375    -1.91   0.056    -.0825787    .0010626
q11_how_satisfied_with_life_very |   .0433576   .0080953     5.36   0.000     .0274911    .0592241
                           _cons |  -4.115413   1.203707    -3.42   0.001    -6.474635   -1.756191
--------------------------------------------------------------------------------------------------

Sorry for not sharing the results. So, if I have these coefficients, how should I interpret them ? e.g. an increase of 1% in "q11_how_satisfied_with_life_very" implies exp (0,043)=1,04 - so 4%- increase in my DV?
Regarding the proportions or percentages, how do I know if I'm talking about one or other? my DV is between 0 and 1.

I used the margins like the following. How should I interpret my model? the exp(coefficients) are not the same of the margins command results.

margins, dyex(_all)

Average marginal effects                          Number of obs   =         44
Model VCE    : Robust

Expression   : Predicted mean givingmoney, predict()
dy/ex w.r.t. : Souci_humankind_much tolerance_at_home_mentioned Justifyied_adultery
               Unemployed_should_take_any_job Do_you_consider_you_religious past_frequence_week_month
               why_people_in_need_unlucky q8_5 q11_how_satisfied_with_life_very

--------------------------------------------------------------------------------------------------
                                 |            Delta-method
                                 |      dy/ex   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------------+----------------------------------------------------------------
            Souci_humankind_much |    .002113   .0293589     0.07   0.943    -.0554294    .0596554
     tolerance_at_home_mentioned |   .0019295   .1093707     0.02   0.986    -.2124331    .2162921
             Justifyied_adultery |   .1853545   .0728582     2.54   0.011     .0425551     .328154
  Unemployed_should_take_any_job |   .2592745   .0912705     2.84   0.005     .0803876    .4381614
   Do_you_consider_you_religious |  -.1759145   .0734185    -2.40   0.017    -.3198122   -.0320169
       past_frequence_week_month |   .1236224   .0384032     3.22   0.001     .0483534    .1988913
      why_people_in_need_unlucky |  -.0367728   .0524393    -0.70   0.483    -.1395519    .0660063
                            q8_5 |  -.1358831    .071117    -1.91   0.056    -.2752699    .0035036
q11_how_satisfied_with_life_very |   .4410024   .0771725     5.71   0.000      .289747    .5922578
--------------------------------------------------------------------------------------------------

Thank you
(Obrigado Marcos! Abraços, Marcelo)

[Marcos Almeida]

When a variable goes from 0 to 1, such as this DV, it is a proportion. If it goes from zero to 100 it is a percentage.

The margins command you selected is a semielasticity, but the IVs are already in percentage, hence I fail to see any advantage compared to the regular (dy/dx) output.

To end , I don’t know whether it was just a toy example, but if the sample size is 44, it may be rather small.

[marcelo ribeiro]

Thank you for your answer Marcos.
I saw the stata manual on margins and marginsplot, but this command just works for categorical IVs, what's not my case.However, could I keep with the interpretation: increase of 1% in my IV (e.g.

q11_how_satisfied_with_life_very

) implies increase of exp(coefficient) % in my DV? If not, could you please give me an example how to interpret .
Besides VIF test and linkstest checking residuals, can I use the OLS R^2 as an informal indicator of this model? Or how can I find a similar R^2 for glm?
Unfortanetely the information for my IVs are availabe just for the 44 obs of the DV. Should I gave up on this model because of its size or how can I fix it?

Thank you!
Kind regards,

Marcelo

[Marcos Almeida]

With regards to - margins - , it is not true that "this command just works for categorical IVs".

Please see some examples with - at() - under - margins - command.

Theoretically speaking, I gather the interpretation in #3 would be "an increase in 1% of this variable X would increase the DV in 4.3 percentage points.

In general, 9 predictors for 44 observations seem too much and the significant results may be due to overfitting.

With regards to the study design, it is far from my field, and I believe you should discuss with your supervisor/professor.

In spite of the topic being far from my field, I had the impression there might be, potentially, some sort of ecological fallacy as well as overfitting.

[marcelo ribeiro]

Good afternoon Marcos,

Thank you very much for your insights and answers, they were very helpful.

Kind regards,
Marcelo