I am working on ordered Logit. Tried to solve the estimates and proportional odds using R. Is it correct

Question

Question: Have a look at data set Two.csv. It contains a potentially dependent binary variable Y , and two potentially independent variables {X1, X2} for each unit of measurement.

(a) Read data set Two.csv into R and have a look at the format of the dependent variable. Discuss three models which might be appropriate in this data situation. Discuss which aspects speak in favor of each model, and which aspects against.

(b) Suppose variable Y measures financial ratings A : y = 1, B : y = 2, and C : y = 3, that is, the creditworthiness A: high, B: intermediate, C: low for unit of measurement firm i. Model Y by means of an ordered Logit model as a function of {X1,X2} and estimate your model by means of a built-in command.

(c) Explain the proportional odds-assumption and test whether the assumption is critical in the context of the data set at hand.

##a) Read data set Two.csv into R and have a look at the format of the dependent variable.

O <- read.table("C:/Users/DELL/Downloads/ExamQEIII2021/Two.csv",header=TRUE,sep=";")
str(O)
dim(O)
View(O)
 
##b)
library(oglmx)
ologit<- oglmx(y~x1+x2,data=O, link="logit",constantMEAN = FALSE, constantSD = FALSE,
               delta=0,threshparam =NULL)
results.ologis <- ologit.reg(y~x1+x2,data=O)
summary(results.ologis)
## x1  1.46251
## x2 -0.45391
margins.oglmx(results.ologis,ascontinuous = FALSE) #Build in command for AMElogit

##c) Explain the proportional odds-assumption and test whether the assumption is critical
#in the context of the data set at hand.

#ordinal Logit WITH proportional odds(PO)
library(VGAM)
a <- vglm(y~x1+x2,family=cumulative(parallel=TRUE),data=O)
summary(a)

#ordinal Logit WITHOUT proportional odds [a considers PO and c doesn't]
c <- vglm(y~x1+x2,family=cumulative(parallel=FALSE),data=O)
summary(c)

pchisq(deviance(a)-deviance(c),df.residual(a)-df.residual(c),lower.tail=FALSE)
## 0.4936413 ## No significant difference in the variance left unexplained. Cannot
#confirm that PO assumption is critical.

#small model
LLa <- logLik(a)
#large model
LLc <- logLik(c)  
#2*LLc-2*
df.residual(c) 
df.residual(a) #or similarly, via a Likelihood Ratio test.

# or, if you are unsure about the number of degrees of freedom
LL<- 2*(LLc -LLa)
1-pchisq(LL,df.residual(a)-df.residual(c))
## 0.4936413 [SAME AS ## No sign. line]
##Conclusion: Likelihood do not differ significantly with the assumption of non PO.