The paired comparison method for latent variables An Application of - PowerPoint PPT Presentation

The paired comparison method for latent variables An Application of the Bradley Terry Model Almut Thomas Michaela Gareiß Regina Dittrich Reinhold Hatzinger  nd Workshop on Psychometric Computing February  th - February  th  LMU, Department for Statistics Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods Results  Introduction Possible Refinement Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl  ❍ Instrument based on Holland’s (  ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results  Possible Refinement Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl  ❍ Instrument based on Holland’s (  ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results  Possible Refinement I nvestigative : intellectual, scientific Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl  ❍ Instrument based on Holland’s (  ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results  Possible Refinement I nvestigative : intellectual, scientific Results  Comparison of Results A rtistic : creative, independent Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl  ❍ Instrument based on Holland’s (  ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results  Possible Refinement I nvestigative : intellectual, scientific Results  Comparison of Results A rtistic : creative, independent S ocial : supporting, helping Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl  ❍ Instrument based on Holland’s (  ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results  Possible Refinement I nvestigative : intellectual, scientific Results  Comparison of Results A rtistic : creative, independent S ocial : supporting, helping E nterprising : competitive, persuading Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl  ❍ Instrument based on Holland’s (  ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results  Possible Refinement I nvestigative : intellectual, scientific Results  Comparison of Results A rtistic : creative, independent S ocial : supporting, helping E nterprising : competitive, persuading C onventional : detail-oriented, organizing Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results  Possible Refinement Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results  Build a greenhouse (R) grow and maintain ◦ ◦ Possible Refinement rare plants (I) Results  in your own garden. Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results  Build a greenhouse (R) grow and maintain ◦ ◦ Possible Refinement rare plants (I) Results  in your own garden. Comparison of Results Play as a musician (A) ◦ ◦ be a conductor (E) in a folk group. Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results  Build a greenhouse (R) grow and maintain ◦ ◦ Possible Refinement rare plants (I) Results  in your own garden. Comparison of Results Play as a musician (A) ◦ ◦ be a conductor (E) in a folk group. Produce (R) ◦ ◦ sale (E) christmas decoration. Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Standard Procedure Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Sum the selected items of each scale Analysing FIT with Paired Comparisons Methods Compare the means of the sub-scales Results  Possible Refinement Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Standard Procedure Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Sum the selected items of each scale Analysing FIT with Paired Comparisons Methods Compare the means of the sub-scales Results  Possible Refinement Each item has a di ff erent attractivity Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Standard Procedure Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Sum the selected items of each scale Analysing FIT with Paired Comparisons Methods Compare the means of the sub-scales Results  Possible Refinement Each item has a di ff erent attractivity Results  Comparison of Results The selection of an item depends on the o ff ered alternative Comparison of sub-scale means is not appropriate Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Way out Introduction ❍ Instrument Use of methods for Paired Comparisons ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods Results  Possible Refinement Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Way out Introduction ❍ Instrument Use of methods for Paired Comparisons ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods Results  FIT: Possible Refinement Results   di ff erent items Comparison of Results  di ff erent items for each sub-scale  comparisons e.g. R  : I  , I  : A  , Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate ❍ Categorical Object Covariates ❍ Reparameterization Matrix Analysing FIT with Paired ❍ Including Subject Covariates ❍ Sample Comparisons Methods ❍ Solution Results  Possible Refinement Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Problem Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate [R  ] [I  ] [I  ] [A  ] [A  ] [S  ] ... ❍ Categorical Object Covariates [R  ]  -      ... ❍ Reparameterization Matrix [I  ] -       ❍ Including Subject Covariates [I  ]    -    ❍ Sample [A  ]   -     ❍ Solution Results  [A  ]      -  Possible Refinement [S  ]     -   Results  ... ... Comparison of Results Linear dependencies in the design matrix Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Object Covariate Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate ❍ Categorical Object Covariates ❍ Reparameterization Matrix ❍ Including Subject Covariates ❍ Sample ❍ Solution Each sub-scale is treated as an object: R I A S E C Results  Possible Refinement Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 

Object Covariate Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate ❍ Categorical Object Covariates ❍ Reparameterization Matrix ❍ Including Subject Covariates ❍ Sample ❍ Solution Each sub-scale is treated as an object: R I A S E C Results  Possible Refinement Each item is assigned to a sub-scale Results  Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables – 