I am getting the exact same results for a probit regression and post-hoc tests (simultaneous tests for linear hypotheses) - is this because I have used a dummy variable in the probit model and so it is effectively comparing each factor level to the reference group thus when I run the post-hoc, which is comparing differences between the two groups, that I get the same answers?

This is the model I fitted:


and this is the post hoc test that I did:

 summary(glht(m1, lsm(pairwise ~ Name.Origin)))
  • $\begingroup$ It would be impossible for anyone to answer this question if you don't tell what model you fitted. $\endgroup$
    – Russ Lenth
    Aug 19 '15 at 22:00
  • $\begingroup$ @rvl I have added the model and post hoc tests - thank you $\endgroup$
    – Lola2000
    Aug 19 '15 at 22:12
  • $\begingroup$ The 'question' is uninterpretable here. Also, this seems to be a logit model. $\endgroup$ Aug 19 '15 at 22:36
  • $\begingroup$ @rvl managed to interpret and answer it but thanks for the pick up on the error in the code which I have edited $\endgroup$
    – Lola2000
    Aug 20 '15 at 10:34

The default parameterization of factors in R uses contr.treatment, which generates indicator variables for all but the first treatment. With that parameterization, the regression coefficients are estimates of the difference (on the probit scale in this example) between the (second, third, ... last) factor levels and the first one. Those will be exactly the results in the first several pairwise comparisons in the glht results, except the signs will be reversed. Moreover, their standard errors and $t$ statistics will match.

  • $\begingroup$ Thank you @rvl, this is exactly what I was trying to ask - sorry if it was initially unclear. When you say 'estimates of the difference', if, for example, the regression coefficient for the second factor level was -0.629 and so in the post hoc is 0.629 - how is this practically interpreted in relation to the first level? As I understand, you cannot really interpret them in a meaningful way (which is where marginals could come in) but rather look at the direction etc. ? $\endgroup$
    – Lola2000
    Aug 20 '15 at 10:46
  • $\begingroup$ All these have to do with the linear-predictor scale. The model predicts the value of $\Phi^{-1}(p_i)$ where $p_i$ is the probability of success at the $i$th setting of the factor, and $\Phi^{-1}$ is the inverse of the standard normal CDF (the probit function). Your regression coefficient of $-.629$ is an estimate of $\Phi^{-1}(p_2)-\Phi^{-1}(p_1)$. $\endgroup$
    – Russ Lenth
    Aug 20 '15 at 16:36

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