INTRO TO
GENERALIZED LINEAR MIXED MODELING
Outline
LINEAR MODELS
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Equation: Y = Xβ + ε
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Assumptions:
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Linearity
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Homoscedasticity
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Normal residuals
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Independent observations
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LINEAR MODELS
LINEAR MODELS
No handling of:
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Correlated data (e.g., repeated measures)
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Hierarchical structure
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Non-normal data (e.g., binary, count)
LINEAR MODELS
No handling of:
-
Correlated data (e.g., repeated measures)
-
Hierarchical structure
-
Non-normal data (e.g., binary, count)
GENERALIZED LINEAR MODELS
Equation: g(E[Y])=Xβg(\mathbb{E}[Y]) = X\betag(E[Y])=Xβ
- Key: Link function ggg
Link function matters!
LINEAR MIXED MODELS
- Old Equation: Y = Xβ + ε
- Equation: Y=Xβ+Zb+εY = X\beta + Zb + \varepsilonY=Xβ+Zb
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New term: ZbZbZb = random effects
- Clustering
- Repeated Measures
LINEAR MIXED MODELS
LINEAR MIXED MODELS
LM Report
LMM Report
LINEAR MIXED MODELS
LM Report
LMM Report
GENERALIZED LINEAR MIXED MODELS
Equation: g(E[Y])=Xβg(\mathbb{E}[Y]) = X\betag(E[Y])=Xβ +Zb
ZbZbZb = random effects
- Key: Link function ggg
GENERALIZED LINEAR MIXED MODELS
GENERALIZED LINEAR MIXED MODELS
Equation: g(E[Y])=Xβg(\mathbb{E}[Y]) = X\betag(E[Y])=Xβ +Zb
ZbZbZb = random effects
- Key: Link function ggg
GENERALIZED LINEAR MIXED MODELS
Equation: g(E[Y])=Xβg(\mathbb{E}[Y]) = X\betag(E[Y])=Xβ +Zb
ZbZbZb = random effects
- Key: Link function ggg
SUMMARY
THANKS!
GLMM
By Safa Andac
