看完后觉得关键的几个地方不太理解，英文理解很模糊，求助高手帮忙看看，这个几步的结果中关键边际效应的核心意思是什么，声明下，并非本人偷懒不看英文，而是英文单词句法90%都懂，可就是它所表达的意思我不理解，恳请耗时帮助，十分十分十分感谢啦！

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opened on:11 May 2015, 23:49:00

第一步：logit回归（这步没什么问题）———— logit grade gpa tuce i.psi, nolog

Logistic regression Number of obs = 32
LR chi2(3) = 15.40
Prob > chi2 = 0.0015
Log likelihood = -12.889633 Pseudo R2 = 0.3740

------------------------------------------------------------------------------
grade | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gpa | 2.826113 1.262941 2.24 0.025 .3507938 5.301432
tuce | .0951577 .1415542 0.67 0.501 -.1822835 .3725988
1.psi | 2.378688 1.064564 2.23 0.025 .29218 4.465195
_cons |-13.02135 4.931325 -2.64 0.008 -22.68657 -3.35613
------------------------------------------------------------------------------


第二步：求边际效应（看贴说明，边际效应的概念是自变量变1单位时，预测概率变化的程度，“预测概率到底是神马意思！？，而且这个结果是0.4左右，会有这么大么！？求帮助１）———— margins, dydx(*) atmeans

Conditional marginal effects Number of obs = 32
Model VCE : OIM

Expression : Pr(grade), predict()
dy/dx w.r.t. : gpa tuce 1.psi
at : gpa = 3.117188 (mean)
tuce = 21.9375 (mean)
0.psi = .5625 (mean)
1.psi = .4375 (mean)

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gpa | .5338589 .237038 2.25 0.024 .069273 .9984447
tuce | .0179755 .0262369 0.69 0.493 -.0334479 .0693989
1.psi | .4564984 .1810537 2.52 0.012 .1016397 .8113571
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

Discrete Change for Categorical Variables. Categorical variables, such as psi, can only take
on two values, 0 and 1. It wouldn’t make much sense to compute how P(Y=1) would change if,
say, psi changed from 0 to .6, because that cannot happen. The MEM for categorical variables
therefore shows how P(Y=1) changes as the categorical variable changes from 0 to 1, holding all
other variables at their means. That is, for a categorical variable Xk
Marginal Effect Xk = Pr(Y = 1|X, Xk = 1) – Pr(y=1|X, Xk = 0)
In the current case, the MEM for psi of .456 tells us that, for two hypothetical individuals with
average values on gpa (3.12) and tuce (21.94), the predicted probability of success is .456 greater
for the individual in psi than for one who is in a traditional classroom. To confirm, we can easily
compute the predicted probabilities for those hypothetical individuals, and then compute the
difference between the two.

第三步：求某一分类变量的边际效应么！？（这里有些完全不懂了，帖子意思是求这个边际效应时，其他变量在均值位置么！？这个结果怎么解释！？）———— . margins psi, atmeans

Adjusted predictions Number of obs = 32
Model VCE : OIM

Expression : Pr(grade), predict()
at : gpa = 3.117188 (mean)
tuce = 21.9375 (mean)
0.psi = .5625 (mean)
1.psi = .4375 (mean)

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
psi |
0| .1067571 .0800945 1.33 0.183 -.0502252 .2637393
1| .5632555 .1632966 3.45 0.001 .2432001 .8833109
------------------------------------------------------------------------------

For categorical variables with more than two possible values, e.g. religion, the marginal effects
show you the difference in the predicted probabilities for cases in one category relative to the
reference category. So, for example, if relig was coded 1 = Catholic, 2 = Protestant, 3 = Jewish, 4
= other, the marginal effect for Protestant would show you how much more (or less) likely
Protestants were to succeed than were Catholics, the marginal effect for Jewish would show you
how much more (or less) likely Jews were to succeed than were Catholics, etc.
Keep in mind that these are the marginal effects when all other variables equal their means
(hence the term MEMs); the marginal effects will differ at other values of the Xs.
Instantaneous rates of change for continuous variables. What does the MEM for gpa of
.534 mean? It would be nice if we could say that a one unit increase in gpa will produce a .534
increase in the probability of success for an otherwise “average” individual. Sometimes
statements like that will be (almost) true, but other times they won’t. For example, if an
“average” individual (average meaning gpa = 3.12, tuce = 21.94, psi = .4375) saw a one point
increase in their gpa, here is how their predicted probability of success would change:

. margins, at(gpa = (3.117188 4.117188)) atmeans

Adjusted predictions Number of obs = 32
Model VCE : OIM

Expression : Pr(grade), predict()

1._at : gpa = 3.117188
tuce = 21.9375 (mean)
0.psi = .5625 (mean)
1.psi = .4375 (mean)

2._at : gpa = 4.117188
tuce = 21.9375 (mean)
0.psi = .5625 (mean)
1.psi = .4375 (mean)

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1| .2528205 .1052961 2.40 0.016 .046444 .459197
2| .8510027 .1530519 5.56 0.000 .5510265 1.150979
------------------------------------------------------------------------------

For categorical variables with more than two possible values, e.g. religion, the marginal effects
show you the difference in the predicted probabilities for cases in one category relative to the
reference category. So, for example, if relig was coded 1 = Catholic, 2 = Protestant, 3 = Jewish, 4
= other, the marginal effect for Protestant would show you how much more (or less) likely
Protestants were to succeed than were Catholics, the marginal effect for Jewish would show you
how much more (or less) likely Jews were to succeed than were Catholics, etc.
Keep in mind that these are the marginal effects when all other variables equal their means
(hence the term MEMs); the marginal effects will differ at other values of the Xs.
Instantaneous rates of change for continuous variables. What does the MEM for gpa of
.534 mean? It would be nice if we could say that a one unit increase in gpa will produce a .534
increase in the probability of success for an otherwise “average” individual. Sometimes
statements like that will be (almost) true, but other times they won’t. For example, if an
“average” individual (average meaning gpa = 3.12, tuce = 21.94, psi = .4375) saw a one point
increase in their gpa, here is how their predicted probability of success would change:

第四步：求某一连续变量的边际效应么！？（这里有些完全不懂了，为什么要设定在某一区间内完成！？）———— . margins, at(gpa = (3.117188 3.118188)) atmeans noatlegend

Adjusted predictions Number of obs = 32
Model VCE : OIM

Expression : Pr(grade), predict()

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1| .2528205 .1052961 2.40 0.016 .046444 .459197
2| .2533548 .1053672 2.40 0.016 .0468388 .4598707
------------------------------------------------------------------------------

Note that (a) the predicted increase of .598 is actually more than the MEM for gpa of .534, and
(b) in reality, gpa couldn’t go up 1 point for a person with an average gpa of 3.117.
MEMs for continuous variables measure the instantaneous rate of change, which may or may
not be close to the effect on P(Y=1) of a one unit increase in Xk. The appendices explain the
concept in detail. What the MEM more or less tells you is that, if, say, Xk increased by some
very small amount (e.g. .001), then P(Y=1) would increase by about .001*.534 = .000534, e.g.

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closed on:11 May 2015, 23:50:31
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