Dear Statalisters,

Here I have a statistical question, related to I believe trend test, for a substantive problems. In public health literature, the SES-health gradient is quite well-konwn; that is as one's SES level increases, so does his/her health status. So suppose here I have an income variable with, say four levels, corresponding to first, second, third, and fourth quartiles, and I use the fourth quartile as the reference category with Q1, Q2, Q3 as the dummy indicators for the first three levels. To simplify, I will just have a bivariate linear regression model with only dummy variables on the right hand side, where y* is this latent variable with higher values denoting poorer health status

y* = b0+ b1Q1 + b2Q2 + b3Q3 + e

One way to see if the gradient holds is to test if 1) b1, b2, and b3 are all positive and significantly different from zero; 2) b1 is greater than b2 and b3; and 3) b2 is greater than b3 all simultaneously. Here I can use different options, for example, an awkward one would be the Bonferroni correction.

I am wondering if there is any trend test I can use here to show that the coefficients, from b1 to b3, reduce their magnitude in a roughly linear trend, and how to do that in Stata. Thanks a lot!

Jun Xu, PhD

Professor and Graduate Director

Department of Sociology

Ball State University

Here I have a statistical question, related to I believe trend test, for a substantive problems. In public health literature, the SES-health gradient is quite well-konwn; that is as one's SES level increases, so does his/her health status. So suppose here I have an income variable with, say four levels, corresponding to first, second, third, and fourth quartiles, and I use the fourth quartile as the reference category with Q1, Q2, Q3 as the dummy indicators for the first three levels. To simplify, I will just have a bivariate linear regression model with only dummy variables on the right hand side, where y* is this latent variable with higher values denoting poorer health status

y* = b0+ b1Q1 + b2Q2 + b3Q3 + e

One way to see if the gradient holds is to test if 1) b1, b2, and b3 are all positive and significantly different from zero; 2) b1 is greater than b2 and b3; and 3) b2 is greater than b3 all simultaneously. Here I can use different options, for example, an awkward one would be the Bonferroni correction.

I am wondering if there is any trend test I can use here to show that the coefficients, from b1 to b3, reduce their magnitude in a roughly linear trend, and how to do that in Stata. Thanks a lot!

Jun Xu, PhD

Professor and Graduate Director

Department of Sociology

Ball State University

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