just tallying my results

[Mahnoor Sohail]

Survey: Probit regression
Number of strata =	3	Number of obs =	527
Number of PSUs =	19	Population size =	3,719,863
	Design df =	16
	F( 5, 12) =	.
	Prob > F =	.
	Linearized
schoolenroll3	Coef.	Std. Err. t P>t	[95% Conf.	Interval]
1.male	-.0885022	.0240079 -3.69 0.002	-.1393966	-.0376079
HeightZscor	.2242943	.0418715 5.36 0.000	.1355307	.313058
male#c.HeightZscor
1	-.2325459	.0393101 -5.92 0.000	-.3158796	-.1492122
c.HeightZscor#c.HeightZscor	-.0196331	.007633 -2.57 0.020	-.0358143	-.0034519

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Hello,
i have this probit model.
Dep variable is a dummy variable, school enrollment.
Regressors are:
male is a dummy
HeightZscore is a contionous variable representing child's health.

i did
quietly margins, at ( HeightZscoreP=(-5(1)6)) over (male)
marginsplot
to get the marginal effect of Height score separately for males and females and for the whole sample GRAPHS ATTACHED


I did simulations to the sample, improving child's health while keeping every other regressor as it is to see the effect on the predicted probability of school enrollment.
so the effect on simulations of (80%, 85%, 90% 95% of the median height of children)--representing the effect of a successful nutrition program on the prob of school enrollment.

For males: the average of predicted probability keeps on decreasing
females: decreases and then increases
total: decreases then increases

so the graphs support that it does have a non linear relationship
I want to know the effect of simulations (improving height) on predicted probability are they supporting the non linear relation?

[Clyde Schechter]

Your probit model is probably mis-specified. When you represent HeightZscor with a quadratic term and you do an interaction with male, you almost certainly need to include an interaction between male and the quadratic term as well. It is not, strictly speaking, illegal to interact only with the linear term, but what it creates is a very bizarre kind of interaction. The reason is that in a quadratic model, the linear coefficient is meaningless. It does not correspond to any effect of anything. In a quadratic model, the linear coefficient is a part of the expression that determines the location of the axis of the parabola, but it is only a part of that expression, so it is not possible to even characterize what that interaction term means. Moreover, by failing to interact with the quadratic term, you are imposing the constraint that the male and female parabolas must have the same "width," which is a very strong constraint for which there is seldom if ever any supporting evidence, and which is unlikely to be true in most situations.

So before you proceed, I suggest you re-run your -probit- model adding in the male-quadratic term interaction. The simplest way to be sure you get this right is to use the ## operator:

probit schoolenroll3 i.male##c.HeightZscor##c.HeightZscor

Finally, I am not sure what kind of simulations you preformed, so it is difficult to know how they relate to your model.

Added: Are you sure you want the -over(male)- option in your margins command? If you think that this is a way of adjusting for the confounding effects of sex, you have it wrong. Rather it does separate estimations for males and females: it does not in any way attempt to balance the distributions of the other variables among males and females. If you want adjusted results, where males and females are made to be comparable in other respects, the code is:

margins male, at(HeightZsco = (-5(1)6)

[Mahnoor Sohail]

thank you so much!! really
now just a small question i know you always say not to look at the p value or significance then how will i interpret the quadratic term as now it has become insignificant

	Linearized
schoolenroll3	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
1.male	-.6290041	.043407	-14.49	0.000	-.7210229	-.5369853
HeightZscoreP	.2202618	.0399163	5.52	0.000	.1356429	.3048806
male#c.HeightZscoreP
1	-.3628218	.060764	-5.97	0.000	-.4916358	-.2340078
c.HeightZscoreP#c.HeightZscoreP	-.0006576	.0085042	-0.08	0.939	-.0186856	.0173704
male#c.HeightZscoreP#c.HeightZscoreP
1	-.0350997	.0219784	-1.60	0.130	-.0816918	.0114924

[Clyde Schechter]

So, quadratic models are complicated, and all the more so when you have an interaction term. You cannot assess anything about the importance of the quadratic term from looking only at the quadratic term coefficient, or even at the quadratic coefficient and its interaction with male alone.

In what follows, I assume that the relevant range of values of HeighZscoreP is from -5 to 6, because those are the values you chose in your -margins- command earlier. So the important thing to assess is whether the model suggests that these parabolas have turning points in (or near) that range. The location of the turning point (vertex) of the parabola y = ax² + bx + c is at x = -b/2a. In your case, for females, b = 0.2202618 and a = -.00065676, which places the vertex at HeightZScoreP = 167.5 which is clearly extremely far from the range of values of HeightZscoreP that matter. In other words, for females, the "parabola" is really just a minor curvature departure from a straight line with slope 0.2202618 in the range of values of HeightZscoreP that matter. So you have what is, for practical purposes, a linear, non-quadratic relationship in females. But in males, the coefficients are b = 0.2202618-0.3628218, and a = -0.0006576 - 0.0350997, so the vertex lies at -1.99, which is well within the range of interesting values of HeightZscoreP, in fact rather close to the center.

So what you have here is a very interesting model in which the relationship to HeightZscoreP is linear for females, but definitely quadratic for males. I suggest you visualize this directly by running:

margins male, at(HeightZscoreP = (-5(1)6))
marginsplot

[Mahnoor Sohail]

Yes Clyde Schechter !! Thank you thank you thank you!