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I am using the vglm function in R to compute the effect of my independent variable on my dependent variables (ranging from -2 to 2). I also receive output for my computations. However, I do not completely understand what the reference value for the comparisons are. Does the function compare the 2 vs. 1,0,-1,-2 responses in GenderMale:1 and in GenderMale:2 the 2,1 vs. 0,-1,-2 responses or how can I interpret the output?

Call:
    vglm(formula = compensate ~ Gender, family = cumulative(parallel = FALSE), 
        data = my_data)
    
    Coefficients: 
                  Estimate Std. Error z value Pr(>|z|)    
    (Intercept):1  -2.7141     0.3113  -8.717  < 2e-16 ***
    (Intercept):2  -1.0761     0.1726  -6.234 4.54e-10 ***
    (Intercept):3  -0.3307     0.1524  -2.170  0.03002 *  
    (Intercept):4   1.4733     0.1930   7.634 2.28e-14 ***
    GenderMale:1   -1.3406     0.6602  -2.031  0.04230 *  
    GenderMale:2   -1.0357     0.2980  -3.475  0.00051 ***
    GenderMale:3   -0.2784     0.2194  -1.269  0.20441    
    GenderMale:4    0.1091     0.2783   0.392  0.69499    
    ---
    Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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  • $\begingroup$ Could you explain what you mean by "cut off points"? $\endgroup$
    – whuber
    Apr 21, 2021 at 18:06
  • $\begingroup$ Maybe cut off point is the incorrect word here but from what I understood is that the coefficients (e.g. :1) indicate a comparison between two responses. My question now relates to how the vglm function uses these comparisons on an integer dependent variable. Does the :1 mean that the significance of gender is compared on the answers -2 and 2 and for :2 the answers -1 and 2 or am I misinterpreting the output of the function here? $\endgroup$
    – Annanas
    Apr 21, 2021 at 19:05
  • $\begingroup$ One would suppose the suffixes refer to four components of your response variable. $\endgroup$
    – whuber
    Apr 21, 2021 at 19:06
  • $\begingroup$ Ok, I would understand that. But the suffixes are always the same in that case no matter if my answer variable is (-2 to 2) or (0-4). For this reason, I have difficulty understanding how the suffixes are related to the answers. $\endgroup$
    – Annanas
    Apr 21, 2021 at 19:08
  • 1
    $\begingroup$ (Intercept):1 corresponds to the parameter $\beta_{0_1}$ and so on in description of the third parameterisation of the proportional odds model at stats.stackexchange.com/a/38130/77222 $\endgroup$ Apr 21, 2021 at 19:43

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