# What is the relationship between ordinary least squares and poisson model?

I am a beginner in learning Statistics with some knowledge of machine learning, some concepts really confused me recently.

Starting from the linear regression and OLS, I think the former is a model with parameters/coefficient and the latter is the method I used to estimate the parameters for the linear regression model. So the relationship between them is the model and estimating method.

However, I read papers using the Gravity Model to describe some phenomena or test hypotheses, some of them estimate the parameters by OLS, but the others use "models" like Poisson, negative binomial to "estimate" the parameters.

I am confused, how can I use one "model" to estimate the parameters of another?

It must be something wrong with my concepts system, and I really need someone to correct me.

In addition, I want to use econometrics methods/models to perform my research (not in the field of statistics or econometrics), is there any books with practical examples and code I can read? Since textbooks I read pay a lot of attention to prove something and lack a macro view of the whole system, I am still not able to perform actual experiments even I obtain that knowledge. Maybe books with some end-to-end examples can help.

• Hi: A regression model is used when the model is linear and the error term is normally distributed. For other assumed distributions ( poisson, binomial whatever ), there are generalized linear models which can be viewed as generalizations of regression models. I would look at a book or notes on glms for a detailed explanation of them. John Fox has a textbook that does a pretty good job with glm's. There are also specific texts just focus on glm's but, I think, for someone starting out, John's book would be a good starting point. Also, I'm sure there should be notes on the internet. Mar 17 '20 at 5:21
• @mlofton Thanks! But I still don't know which category should Gravity Model, OLS, Poisson, and binomial fall in. According to your comment, Poisson and binomial are GLMs, what about OLS? How can I use GLMs to estimate the parameter of another model (like Gravity Model)? Could you elaborate? Thanks again! Mar 17 '20 at 5:40
• @mlofton Instead of the regression model, what are the others and where they locate in the system of econometrics? I can't find books on this topic. Mar 17 '20 at 5:46
• You may find Gravity Model of International Trade: A User Guide by Ben Shepherd illuminating. See the section on Alternative Estimators in particular. There are Stata and R versions of the code as well. Mar 18 '20 at 6:16