Dear researchers,
I am new to this great website, and this is my first post, and I hope to receive an answer to my questions, please.

I have a panel dataset for a set of firms for the period extending from 2000-2010. I have a categorical variable, which is a firm score, which is the dependent variable. This score consists of five scales. For instance, score 1 means very poor, 2 poor, 3 good, 4 very good, and 5 Excellent. Let’s take company A as an example. It might have a score of 3 in the year 2000, and 4 in 2001, and 5 in 2008. I mean it is not necessary to have the same code in each year for the firm.

My independent variables include continuous, binary, and categorical variables.

To be honest, I have read about which is the correct way to do the analysis, ordered logit or multinomial logit? I have found that we need to use the ordered logit regression as the dependent variable takes a number of finite and discrete values that contain ordinal information. However, the multinomial don’t contain ordinal information.

HOWEVER, the literature has mentioned that this score is changing over time and thus they can’t be compared across years. Thus, to address this issue, they have used the following equation which is:
(firm rank ‒ 1)/(number of firms e 1)
This gives the annual percentile rank of the dependent variable ranging between 0 and 1 each year. Thus, in that way, I should use the logistic regression.

My questions, please:
What is the code for performing the ordinal logit regression?
What is the code for performing the logit regression?
What is the correlation analysis code in both above two analyses?
Can I use the lag independent variables in the ordinal logit regression and the logit regression?

Many thanks in advance.