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Created:
Nov 19, 2021 12:44 PM
| Last Modified: Oct 24, 2023 10:40 AM
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glm examples.jrn
Background:
Simple Linear Regression assume errors (and response) are normal, but when normality isn't the case, predictions may fall outside of meaningful range (maybe not a big deal) and inference is not reliable (probably a bigger deal)
Generalized Linear Models (GLM) assume some other distribution than normality, for example for:
Count data (e.g., number of defects on a product)
Skewed data (e.g., salaries)
Proportions
Labels (e.g., good/neutral/bad or yellow/blue/green)
Generalized Linear Models (GLM) have three ingredients
A distribution for the response given the predictors (the random piece)
A linear predictor (the systematic piece)
A link function (the piece that random and systematic pieces)
Use the R-square to compare models within a distribution.
Use AICc and BIC (information criteria.) to compare between distributions
AICc and BIC estimate the Kullback-Leibler divergence, which is the distance from the fitted model to the truth
Use them to compare models within the same distribution and across different distributions
Rule of thumb: AIC tends to overfit and BIC tends to underfit
General guidelines for choosing Distributions for Continuous Response
Do we have negative values? Use normal
Is it bound to (0,1)? Use beta
Does variance increase with the mean? Use gamma, Weibull, lognormal
Is it time-to-event/censored? Probably use Weibull or lognormal
A pretty good catch-all? Use normal
Do we suspect that we have outliers? Use Cauchy or t(5)
Choosing Distribution when response isn’t numeric
Is it two-level? Use the binomia; (e.g., Yes/No or A/B)
Is it 3+ levels and order matters? Use Ordinal logistic. (eg., Low/Medium/High or Small/Medium/Large
Is it 3+ levels and order doesn’t matter? Use the Multinomial (e.g.,Pizza/Hamburger/Burrito or Red/Blue/Green/Orange)
See how to choose, specify and build, compare, and evaluate models using Generalized Regression in JMP Pro. Q&A and is included throughout the presentation.
Can you use zero inflated for an inverse problem, where you have a lot of extreme high measures?
I typically look at reaction times, which tend to follow an ex-Gaussian distribution. That distribution is a conflation of an exponent and normal. Recommendations for model to use: Gamma, exponential?
Can we run a GLMM (with a random effect in the model) in JMP?
Yes, it is in JMP Pro 17 currently used by Early Adopters.
For the gamma, does JMP display lamda & variance?
Is there a way to use the Simulate feature in JMP Pro to do a Power analysis for an Ordinal Logistic model?
Does the simulate column have a random component?
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