Dear members of the list,
For a sample of highly educated young adults in 24 countries that participated in PIAAC survey, I estimate the probability of attaining a master level degree instead of a bachelor level one. Thus, my dependent variable is dichotomous. My key independent variable is father's education, which is a variable with three categories, corresponding to basic, intermediate and higher education. Controlling for gender and age, I want to estimate the effect of father's education on the attainment of a higher level degree (master) instead of a lower level one among the individuals in the sample. This is my model:
In principle, my results show that father's education has an statistically significant effect on the probability of attaining a master level degree instead of a bachelor level one. See coefficients corresponding to ISCED 3/4 and ISCED 5/6 in the following table:
Next, I proceed to estimate the average marginal effect of different categories of father's education on the probability of attaining a master level degree instead of a bachelor one:
I do not understand why, if the effect is statistically significant in the results (table above), the confidence intervals in the graph overlap. See next:
Is there anyone who could help me to understand the correspondence between the statistical significance of the coefficients in the table and the overlap of the confidence intervals in the graph? Which one of these results should I credit?
Many thanks for your attention
Kind regards
Luis Ortiz
For a sample of highly educated young adults in 24 countries that participated in PIAAC survey, I estimate the probability of attaining a master level degree instead of a bachelor level one. Thus, my dependent variable is dichotomous. My key independent variable is father's education, which is a variable with three categories, corresponding to basic, intermediate and higher education. Controlling for gender and age, I want to estimate the effect of father's education on the attainment of a higher level degree (master) instead of a lower level one among the individuals in the sample. This is my model:
PHP Code:
xtmelogit univ i.edufath female age  cntryid3:
In principle, my results show that father's education has an statistically significant effect on the probability of attaining a master level degree instead of a bachelor level one. See coefficients corresponding to ISCED 3/4 and ISCED 5/6 in the following table:
PHP Code:
Fitting comparison model:
Iteration 0: log likelihood = 12825.158
Iteration 1: log likelihood = 12512.74
Iteration 2: log likelihood = 12511.102
Iteration 3: log likelihood = 12511.102
Fitting full model:
tau = 0.0 log likelihood = 12511.102
tau = 0.1 log likelihood = 11306.365
tau = 0.2 log likelihood = 11278.014
tau = 0.3 log likelihood = 11276.239
tau = 0.4 log likelihood = 11317.484
Iteration 0: log likelihood = 11258.67
Iteration 1: log likelihood = 11162.029
Iteration 2: log likelihood = 11153.553
Iteration 3: log likelihood = 11153.329
Iteration 4: log likelihood = 11153.329
Randomeffects logistic regression Number of obs = 19,663
Group variable: cntryid3 Number of groups = 24
Random effects u_i ~ Gaussian Obs per group:
min = 320
avg = 819.3
max = 3,302
Integration method: mvaghermite Integration pts. = 12
Wald chi2(4) = 340.00
Log likelihood = 11153.329 Prob > chi2 = 0.0000

master  Coef. Std. Err. z P>z [95% Conf. Interval]
+
edufather 
ISCED 3/4  .1350686 .0466318 2.90 0.004 .0436719 .2264653
ISCED 5/6  .6315997 .0445544 14.18 0.000 .5442747 .7189247

female  .0768024 .0331973 2.31 0.021 .1418679 .011737
age  .0336828 .003584 9.40 0.000 .0266582 .0407073
_cons  2.447529 .3277209 7.47 0.000 3.08985 1.805208
+
/lnsig2u  .6325732 .304019 .0367069 1.228439
+
sigma_u  1.372023 .2085606 1.018523 1.848214
rho  .3639468 .0703772 .2397336 .5093969

LR test of rho=0: chibar2(01) = 2715.55 Prob >= chibar2 = 0.000
Next, I proceed to estimate the average marginal effect of different categories of father's education on the probability of attaining a master level degree instead of a bachelor one:
PHP Code:
margins edufather, predict(mu fixedonly) vsquish level(95) post
marginsplot
I do not understand why, if the effect is statistically significant in the results (table above), the confidence intervals in the graph overlap. See next:
Is there anyone who could help me to understand the correspondence between the statistical significance of the coefficients in the table and the overlap of the confidence intervals in the graph? Which one of these results should I credit?
Many thanks for your attention
Kind regards
Luis Ortiz
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