This week we had no meetings as a class so there was no new information to summarize.
Because of this, I will use this weeks Rpub to review the equation structure models we’ve discussed over the course of the semester.
This is the most common and simple type of regression structure.
It is characterized by a numeric response variable and an intercept and explanatory variable.
\[Y_i = \beta_0 + \beta_1(X_i)\]
This is similar to a linear model except the response is binary.
We would use logistic regression to model data that meets GLM criteria.
\[log(\frac{p_i}{1-p_i}) = \beta_0 + \beta_1(X_i)\]
This is the same scenario as binomial GLM where we have a non-normal response type.
The only difference is that this time we have a response variable that follows a Poisson distribution.
For example our response may be number of Covid cases in a town, number of whales spotted, etc…
Really any observational data that has a integer counts falls into this category of Poisson
\[log(Y_i) = \beta_0 + \beta_1(X_i)\]
This is a twist on the linear model where within the data we have correlation to account for.
There are a variety of ways to deal with correlation but we mainly talked about using random effects.
\[Y_i = \beta_0 + \beta_1(X_i) + u_j\]
This is the exact same structure and response as GLM - Binomial except in this case we have correlation in the data.
\[log(\frac{p_i}{1-p_i}) = \beta_0 + \beta_1(X_i) + u_j\]
This is again very similar to GLM - Poisson but again we have correlation to account for.
\[log(Y_i) = \beta_0 + \beta_1(X_i) + u_j\]