Hi there,

I'm trying to plot an interaction effect by using effect and plot functions that are described in the following blog post: http://data.library.virginia.edu/visualizing-the-effects-of-proportional-odds-logistic-regression/

My model consists of an ordinal (0,1,2,3) dependent variable (SOICAP), two independent variables (TRA and REL) and a couple of controls. The independent variables are discrete, taking values in the range of 0 to 5. Theoretically speaking, imagine that these two ind. variables are two mechanisms that are (each individually) supposed to increase the outcome. However, I'm also interested to test if they always complement each other or there might be some occasions when they generate substitute effects on the outcome. I ran polr function and here is the result:

Coefficients:

Value Std. Error t value

SIZE_centered 0.7102 0.2345 3.0282**

ASSIM_centered 0.6353 0.2840 2.2366*

PRIOR_centered 6.8723 2.1280 3.2295***

SECTORindustrial -0.1389 0.5833 -0.2382

SECTORnatural stone 0.4087 0.6829 0.5985

SECTORconstruction 2.6778 1.1434 2.3419

TRA_centered 0.9997 0.3001 3.3317***

REL_centered 0.6590 0.2559 2.5756**

TRA_REL_centered -0.5858 0.2319 -2.5263**

Intercepts:

Value Std. Error t value

0|1 -0.6726 0.3805 -1.7676

1|2 1.7666 0.4140 4.2670

2|3 4.2472 0.6224 6.8243

Residual Deviance: 155.6056

AIC: 179.6056

So as the coefficients show, the interaction is negative, and we could assume a substitute effect between the two mechanisms. But the plot (attached), as far as I understand it, shows positive interactions since the probability of SOICAP=3 increases dramatically when both TRA and REL increase.

Could anyone please help me out finding what's going on? Am I interpreting the plot correctly?

Best,

Babak