20161017 
 Introduction and Outline of the lecture
 Repetition of the basic ideas of Classical Test Theory (CTT)
 Models of CTT
 The model of essentially tauequivalent variables

Video (Stream)

Slides (Organizational Issues & Repeating the Essentials of Classical Test Theory)
Slides (Model of essentially tauequivalent tests)
Blackboard sketches

20161024 
 The model of essentially tauequivalent variables (continued)
 The role of latent variables in Psychology
 The logit transformation of probabilities
 The definition of the latent variable in the Rasch model
 Rasch homogeneity
 UConditional independence of the items
 An example with Joe and Ann illustrating the Rasch model

Video (Stream)

Slides

20161107 
 Rabix, a program for explorating the Rasch model and the Birnbaum model
 Itemcharacteristic functions
 Likelihood functions
 Estimation of the person parameter using maximum likelihood
 Item information functions
 Test information function
 Standard error function for the estimation of the person parameter
 Identification of the item parameters

Video (Stream)

Slides
Rabix
Blackboard sketch 01
Blackboard sketch 02

20161114 
 The lifesatisfaction data
 Recoding of the negatively formulated items
 Analysis of the lifesatisfaction data with the Rasch modell (WINMIRA)
 Person parameter estimation
 Item parameter estimation

Video (Stream)

Material

20161121 
 Interpretation of the Qstatistics in Winmira for the items
 Bootstrap model test
 Generating data according to the Rasch modell
 Analysis of the generated data with Winmira
 Generating data according to the Birnbaum model
 Analysis of the generated data with Winmira, in particular the Qstatistics and bootstrap procedure
 Generating data according to the Birnbaum model according to a latent variable model with two latent variables
 Analysis of the generated data with Winmira

Video (Stream)

Material
Blackboard sketch 01
Blackboard sketch 02

20161128 
 Summary presentation of the Birnbaum 2PLmodel
 Summary presentation of the Birnbaum 3PLmodel (with guessing parameter)
 Analysis of the life satisfaction scale according to the Rasch model with Mplus
 Discussion of the Mplus Input and Output for this model

Video (Stream)

Slides (The two parameter logistic Birnbaum model)
Slides (The three parameter logistic Birnbaum model)
MplusIn and Outputs
Blackboard sketch 01
Blackboard sketch 02

20161205 
 Specification of the 2PLBirnbaum model in Mplus for the life satisfaction data
 Test of the hypothesis: „The Rasch model holds“ using the Wald test
 Specification of the 2PLBirnbaum model in Mplus for generated data that follow the Birnbaum model.
 Test of the hypothesis: „The Rasch model holds“ using the Wald test for these data that follow the Birnbaum model

Video (Stream)

Material
Blackboard sketch

20161212 
 A first twodimensional IRT model with an own latent variable for the positively and for the negatively formulated items. A first alternative to the Birnbaum model
 Testing the hypothesis: The correlation between the two latent variables is 1.
 The general structural model for the latent variables and the matrices involved in this model.
 An alternative way of testing the hypothesis mentioned above. The regression of Xi2 on Xi1 is perfect. (The variance of the residual is 0).

Video (Stream)

Material
Blackboard sketches

20161219 
 Rasch and Birnbaum analog probit models
 Model test in these models
 A twodimensional probit model
 Data generation according to the Birnbaum analog probit model

Video (Stream)

Material
Blackboard sketches

20170102 
 Link functions and response functions in the logit model and in the probit model
 Assumptions defining the logit model and the probit model
 Factor analytic representation of the probit model
 Relationships between the parameters of different models and parameterizations
 Analysis of the probit model using generated data
 First ideas of item response latent statetrait theory

Video (Stream)

Slides
MplusIn and Outputs
Blackboard sketch 01
Blackboard sketch 02

20170109 
 Basic ideas of latent statetraittheory
 Singletrait model, multistate model and multistatesingletrait model
 Analysis of a probit multistate model with the lifesatisfaction scale (3 times points)
 Analysis of this model with the additional constraint: The correlations of the three latent state variables are equal to 1
 Analysis of a probit singletrait model with the lifesatisfaction scale (3 times points)
 Differences between the last two models

Video (Stream)

MplusIn and Outputs
Blackboard sketches

20170116 
 The Partial Credit Model
 Uconditional thresholdprobabilities
 The two assumptions defining the Partial Credit Model and the definition of the latent variable
 Interpretation of the threshold parameters
 Graphs of the Uconditional thresholdprobabilities for different categories as a function of the latent variable
 Graphs of the Uconditional probabilities for different categories as a function of the latent variable
 Ways of fixing the (version of the) latent variable
 Using the Partial Credit Model for four items of the scale „wellbeing“ of the Multidimensional Mood State Questionnaire with Winmira.
 Interpretation of the output of Winmira

Video (Stream)

WinmiraOutputs
Blackboard sketch

20170123 
 Graded Response Model (GRM) with logit and probit link functions
 Basic assumptions and their implications for the category probabilities
 Thresholds and discrimination parameters in these models
 Application of the probit GRM for the data of the wellbeing scale of the MDMQ at time 1
 Fixing the scale of the latent variables
 Generalizing the probit GRM to a latent state model for three time points

Video (Stream)

Slides (updated 20170127)
MplusIn and Outputs
Blackboard sketch 01
Blackboard sketch 02

20170130 

Video (Stream)

Slides
Blackboard sketch
