How to fix a coefficient in an ordinal logistic regression without proportional odds assumption in R? I want to do an ordinal logistic regression in R without the proportionality odds assumption. I know this can be done directly using vglm() function in R by setting parallel=FALSE.
But my problem is how to fix a particular set of coefficients in this regression setup? For example, say the dependent variable $Y$ is discrete and ordinal and can take values $Y = 1$, $2$, or $3$. If the regressors are $X_{1}$ and $X_{2}$, then the regression equations are
$$ \begin{aligned} 
{\rm logit} \big( P(Y \leq 1) \big) &= \alpha_{1} + \beta_{11}X_{1} + \beta_{12}X_{2} \\
{\rm logit}\big(P(Y \leq 2) \big) &= \alpha_{2} + \beta_{21}X_{1} + \beta_{22}X_{2} 
\end{aligned} $$
I want to set $\beta_{11}$ and $\beta_{22}$ to $1$. Please let me know how can I achieve this. Also if R can't do this, could you also please let me know if I can achieve this in any other statistical software?
 A: I'm not sure I understand what the OP meant when he/she says "I can't use offset because it completely removes the corresponding regressor from the regression." You can fix a parameter using the offset() function in R. I'm using lm() below, but it should work in your model as well.
dat  <- data.frame(x=rnorm(30))
dat$y <- dat$x * 2 + rnorm(30) 
free <- lm(y ~ x,dat)
fixed1<- lm(y ~ offset(2 * x),dat)

summary(free)
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)    
#(Intercept)  0.03899    0.17345   0.225    0.824    
#x            2.17532    0.18492  11.764 2.38e-12 ***

summary(fixed1)
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)
#(Intercept)  0.05043    0.17273   0.292    0.772

The fixed parameter doesn't show up in the output, but it's still fixed at 2. Next I'll fix the x parameter to its estimated value in the free model
fixed2<- lm(y ~ offset(2.17532 * x),dat)
summary(fixed2)
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)
#(Intercept)  0.03899    0.17002   0.229     0.82

Notice the intercept in fixed2 is estimated with the same value as in the free model.
