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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
Annanas
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  • Could you explain what you mean by "cut off points"? – whuber Apr 21 '21 at 18:06
  • 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? – Annanas Apr 21 '21 at 19:05
  • One would suppose the suffixes refer to four components of your response variable. – whuber Apr 21 '21 at 19:06
  • 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. – Annanas Apr 21 '21 at 19:08
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    `(Intercept):1` corresponds to the parameter $\beta_{0_1}$ and so on in description of the third parameterisation of the proportional odds model at https://stats.stackexchange.com/a/38130/77222 – Jarle Tufto Apr 21 '21 at 19:43
  • Thank you, @JarleTufto. This reference helps already a bit. Just to be sure - from what I understood in the answer my above described approach is correct to use the highest response (let's say 2) as reference and then compare the lower responses step by step with this reference? Similar to the example the person in the answer described `'=Good ' vs. observing '=Neutral OR Bad'` – Annanas Apr 21 '21 at 20:28
  • @JarleTufto Just wanted to double check whether I am on the right track. I assume that the highest integer (in this case 2) is the reference category and that I am comparing the variables against this reference, is this correct? – Annanas May 13 '21 at 10:43

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