Module 3: Logistische regressie
MULTIVARIATE
ANALYSE
,Inhoudsopgave
Inhoudsopgave ................................................................................................................................ 1
Module 3: Logistische regressie ..................................................................................................... 3
Logaritmen ...................................................................................................................................... 3
Antilog......................................................................................................................................... 3
Eigenschappen ............................................................................................................................ 3
Andere belangrijke eigenschap ................................................................................................. 4
Natuurlijk logaritme ..................................................................................................................... 4
Odds ............................................................................................................................................... 4
Kansen en odds ........................................................................................................................... 4
Voorwaardelijke odds .............................................................................................................. 4
Odds-ratio (OR) ....................................................................................................................... 5
Standaardfout van OR .............................................................................................................. 5
Logodds-ratio .......................................................................................................................... 6
Betrouwbaarheidsinterval voor OR ........................................................................................... 6
Hypothesetoetsen voor odds-ratios .......................................................................................... 6
Ors in RxC tabellen .................................................................................................................. 7
Logistische regressie ........................................................................................................................ 8
Binaire logistische regressie ......................................................................................................... 8
Lineair probaliteitsmodel ............................................................................................................. 8
Spreidingdiagram: voorspelde waarden – residuën .................................................................... 8
Basisprincipes ............................................................................................................................. 8
Logistische regressie ............................................................................................................... 8
De waarschijnlijkheid ............................................................................................................... 9
ML-schatting ........................................................................................................................... 9
Log-likelihood.......................................................................................................................... 9
Logistische regressiecoëViciënten ........................................................................................... 9
Standaardfouten ................................................................................................................... 10
Voorspelde kans .................................................................................................................... 10
Geen verandering in kans ....................................................................................................... 10
Interactie-eVecten ................................................................................................................. 10
Assumpties bij logistische regressie............................................................................................ 11
Toetsen ..................................................................................................................................... 11
EVecttoets ............................................................................................................................ 11
Wald toets voor categorische variabelen ................................................................................. 11
Toets voor de vergelijking van regressiecoëViciënten in twee onafhankelijke steekproeven ........ 12
Globale toets......................................................................................................................... 12
Pseudo 𝑹𝟐 ............................................................................................................................ 13
Cox & snell 𝑹𝟐 ....................................................................................................................... 13
Nagelkerke 𝑹𝟐 ....................................................................................................................... 13
Interactie-eVecten in logistische regressie .................................................................................. 13
Logistische regressie: uitbreidingen ................................................................................................. 14
Probitregressie .......................................................................................................................... 14
Linkfunctie ............................................................................................................................ 14
Interpretatie .......................................................................................................................... 14
Ordinale logistische regressie ..................................................................................................... 14
Multinomiale logistische regressie .............................................................................................. 14
De multinomiale regressie...................................................................................................... 15
Multinomiale logistische regressie .......................................................................................... 15
Interpretatie coëViciënten...................................................................................................... 15
Toetsen ................................................................................................................................. 16
Het veralgemeend lineair model...................................................................................................... 17
1
, Algmeen lineair model (GLM)...................................................................................................... 17
Veralgemeend lineair model (GLZ) .............................................................................................. 17
Bijvoorbeeld: Lineaire en logistische regressie ........................................................................ 17
Schematische en willekeurige componenten .......................................................................... 17
Voordelen GLZ ....................................................................................................................... 17
Linkfuncties .......................................................................................................................... 18
GLZ ....................................................................................................................................... 18
Distributiefuncties ................................................................................................................. 19
GLM varianten ....................................................................................................................... 19
Voorspelde waarden .............................................................................................................. 19
Fit: likelihoodratio .................................................................................................................. 20
AIC: Akaike information criterion ............................................................................................ 20
BIC: Bayesian information criterion ........................................................................................ 20
Overdispersie ........................................................................................................................ 20
Verdere uitbreidingen GLM ..................................................................................................... 20
2
MULTIVARIATE
ANALYSE
,Inhoudsopgave
Inhoudsopgave ................................................................................................................................ 1
Module 3: Logistische regressie ..................................................................................................... 3
Logaritmen ...................................................................................................................................... 3
Antilog......................................................................................................................................... 3
Eigenschappen ............................................................................................................................ 3
Andere belangrijke eigenschap ................................................................................................. 4
Natuurlijk logaritme ..................................................................................................................... 4
Odds ............................................................................................................................................... 4
Kansen en odds ........................................................................................................................... 4
Voorwaardelijke odds .............................................................................................................. 4
Odds-ratio (OR) ....................................................................................................................... 5
Standaardfout van OR .............................................................................................................. 5
Logodds-ratio .......................................................................................................................... 6
Betrouwbaarheidsinterval voor OR ........................................................................................... 6
Hypothesetoetsen voor odds-ratios .......................................................................................... 6
Ors in RxC tabellen .................................................................................................................. 7
Logistische regressie ........................................................................................................................ 8
Binaire logistische regressie ......................................................................................................... 8
Lineair probaliteitsmodel ............................................................................................................. 8
Spreidingdiagram: voorspelde waarden – residuën .................................................................... 8
Basisprincipes ............................................................................................................................. 8
Logistische regressie ............................................................................................................... 8
De waarschijnlijkheid ............................................................................................................... 9
ML-schatting ........................................................................................................................... 9
Log-likelihood.......................................................................................................................... 9
Logistische regressiecoëViciënten ........................................................................................... 9
Standaardfouten ................................................................................................................... 10
Voorspelde kans .................................................................................................................... 10
Geen verandering in kans ....................................................................................................... 10
Interactie-eVecten ................................................................................................................. 10
Assumpties bij logistische regressie............................................................................................ 11
Toetsen ..................................................................................................................................... 11
EVecttoets ............................................................................................................................ 11
Wald toets voor categorische variabelen ................................................................................. 11
Toets voor de vergelijking van regressiecoëViciënten in twee onafhankelijke steekproeven ........ 12
Globale toets......................................................................................................................... 12
Pseudo 𝑹𝟐 ............................................................................................................................ 13
Cox & snell 𝑹𝟐 ....................................................................................................................... 13
Nagelkerke 𝑹𝟐 ....................................................................................................................... 13
Interactie-eVecten in logistische regressie .................................................................................. 13
Logistische regressie: uitbreidingen ................................................................................................. 14
Probitregressie .......................................................................................................................... 14
Linkfunctie ............................................................................................................................ 14
Interpretatie .......................................................................................................................... 14
Ordinale logistische regressie ..................................................................................................... 14
Multinomiale logistische regressie .............................................................................................. 14
De multinomiale regressie...................................................................................................... 15
Multinomiale logistische regressie .......................................................................................... 15
Interpretatie coëViciënten...................................................................................................... 15
Toetsen ................................................................................................................................. 16
Het veralgemeend lineair model...................................................................................................... 17
1
, Algmeen lineair model (GLM)...................................................................................................... 17
Veralgemeend lineair model (GLZ) .............................................................................................. 17
Bijvoorbeeld: Lineaire en logistische regressie ........................................................................ 17
Schematische en willekeurige componenten .......................................................................... 17
Voordelen GLZ ....................................................................................................................... 17
Linkfuncties .......................................................................................................................... 18
GLZ ....................................................................................................................................... 18
Distributiefuncties ................................................................................................................. 19
GLM varianten ....................................................................................................................... 19
Voorspelde waarden .............................................................................................................. 19
Fit: likelihoodratio .................................................................................................................. 20
AIC: Akaike information criterion ............................................................................................ 20
BIC: Bayesian information criterion ........................................................................................ 20
Overdispersie ........................................................................................................................ 20
Verdere uitbreidingen GLM ..................................................................................................... 20
2
