GLM Flashcards
This is the most common link function for count data
Log
Square root
These are the most common link functions for binomial data
Logit, Probit, comploglog
Types of distributions
Normal, Binomial, Asymptotic, Poisson, Gamma, Weibul, Exponential, Beta, Inverse, Gaussian, Quassipoisson, Quassibinomial
The three elements of a GLM
A Y distribution from the exponential family: Gausian, Binomial, Exponential, Poisson, Gamma.
Linear predictor model
Non-linear link function that can act on both sides of the equation. Inverse on the predictors, Link function on the predicted
MLE
Maximum Likelihood Estimation. Computes a loss function for the distribution
Under this circumstance SSE and MLE are the same
When the distribution is normal/Gaussian
Difference between Generalized Linear Model and General Linear Model
GLM chooses parameters so that the data observed was most likely generated by the model.
General Linear Model chooses the parameters that reduce error the most
Loss function
Computed by MLE and is the difference between a model’s predicted values and the actual values
- LL
Negative log likelihood. Repressent likelihood in a GLM, you want this as negative as possible
x 2 (chi square)
Indicate whether the model is significant or not when compared to the null model (model with no predictors)
-2LL
Is deviance. Follow a distribution of a chi square function
Name the link function:
Gaussian
Identity
Name the link function:
Binomial
Logit
Name the link function:
Poisson
logarithmic / log
Name the link function:
Gamma
Inverse
Name the link function:
Quassi binomial
Logit (the probability of something occuring divided by the probability of not occuring)
Name the link function:
Quassi poisson
log
Inverse link function:
logit
logistic (unlogging the log odds)
Inverse link function:
log
e (exponential but base is e the exponential is the linear formula)
Inverse link function:
Inverse
Inverse
Inverse link function:
Square root
Square
A binomial distribution is common for what kind of data?
Binomial outcome variable. Data that has a floor and a ceiling (proportions/percentages)
A poisson distribution is common for what kind of data?
Count data, dicrete values with lots of 0s inbetween
A gamma distribution is common for what kind of data?
Salaries and latencies or reaction times
How does link and inverse work?
You do a link on the Y side and the inverse on the X side
MLE
Uses a type of loss function
Loss function
Technically SSE is a loss function for normally distributed errors
Why MLE?
So that the data you see is the most likely to have been generated by your model by the selected parameters
Why do you get Zs and not Ts anymore?
Because the relationship between them two. Once you get to a certain sample size they are both the same
You have multiple continuous predictors and a single outcome variable… This is
A multiple regression
You have continuos predictors and categorical predictors… This is….
An ANCOVA
