I have a question about categorical variable regression and post-estimation procedures, not limited to just the use of Stata.
My aim is to estimate the “probability of success” (say, odds-ratio) at an aggregate level using a lower-level dataset; I will use an example to make things clearer.
Suppose we have a dataset, each observation is a student (alumni, to be precise). For each obs, we have information about family wage, IQ, college, and a target categorical variable set to 1 if student successfully graduated. See below the example (fake numbers, of course). My aim is to predict at college level for coming students which is the likelihood she will graduate given certain characteristics.
Let’s say I run a multivariate logit regression using graduation as dependent and college and wage as independent; I get proper coefficients and I can run a post-estimation command to obtain the predicted probability of graduating based on student’s characteristics (pls excuse if I am superquick and inaccurate with terminology).
Now my question: can I estimate the likelihood of graduation at college level? Is it feasible by taking the average (weighted, maybe?) of predicted probability of graduation as computed above? Does it make any sense?
Hope it is clear. Any help will be really appreciated. Thanks. Paolo
My aim is to estimate the “probability of success” (say, odds-ratio) at an aggregate level using a lower-level dataset; I will use an example to make things clearer.
Suppose we have a dataset, each observation is a student (alumni, to be precise). For each obs, we have information about family wage, IQ, college, and a target categorical variable set to 1 if student successfully graduated. See below the example (fake numbers, of course). My aim is to predict at college level for coming students which is the likelihood she will graduate given certain characteristics.
| STUD | COLLEGE | WAGE | IQ | GRADUATION |
| 1 | A | 100 | 105 | 1 |
| 2 | A | 120 | 110 | 0 |
| 3 | A | 210 | 95 | 0 |
| 4 | A | 80 | 84 | 0 |
| 5 | B | 332 | 90 | 1 |
| 6 | B | 321 | 133 | 0 |
| 7 | B | 465 | 144 | 1 |
| 8 | C | 68 | 110 | 0 |
| 9 | C | 77 | 106 | 1 |
| 10 | C | 67 | 101 | 1 |
Let’s say I run a multivariate logit regression using graduation as dependent and college and wage as independent; I get proper coefficients and I can run a post-estimation command to obtain the predicted probability of graduating based on student’s characteristics (pls excuse if I am superquick and inaccurate with terminology).
| STUD | COLLEGE | WAGE | IQ | GRADUATION | PR_GRADUATION |
| 1 | A | 100 | 105 | 1 | 0,92 |
| 2 | A | 120 | 110 | 0 | 0.94 |
| 3 | A | 210 | 95 | 0 | 0.13 |
| 4 | A | 80 | 84 | 0 | 0.09 |
| 5 | B | 332 | 90 | 1 | 0.77 |
| 6 | B | 321 | 133 | 0 | 0.34 |
| 7 | B | 465 | 144 | 1 | 0.86 |
| 8 | C | 68 | 110 | 0 | 0.01 |
| 9 | C | 77 | 106 | 1 | 0.99 |
| 10 | C | 67 | 101 | 1 | 0.65 |
Now my question: can I estimate the likelihood of graduation at college level? Is it feasible by taking the average (weighted, maybe?) of predicted probability of graduation as computed above? Does it make any sense?
| COLLEGE | AVG_GRADUATION | AVG_PR_GRADUATION | ? |
| A | 0.50 | 0.52 | ? |
| B | 0.67 | 0.66 | ? |
| C | 0.67 | 0.55 | ? |
Hope it is clear. Any help will be really appreciated. Thanks. Paolo
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