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## Two families of tree models for multinomial item responses

Fecha: jueves 11 de julio de 2019

Horario: 14:00 a 15:00 hrs.

Lugar: Auditorio Ninoslav Bralic, Facultad de Matemáticas, Pontificia Universidad Católica de Chile**.**

**Relator**: Paul De Boeck, The Ohio State University

**Abstract**:

When more than two response options are available and the response options can be structured as

an option tree, two families of models can be used to model the item response data: probability tree

models and value tree models. Let us take a Likert scale with five response options as an example:

strongly disagree (SD), disagree (D), neutral (N), agree (A), strongly agree (SA). One possible tree is a

linear tree: SD vs. D, N, A, SA; D vs. N, A, SA; N vs. A, SA; A vs SA. Another possible tree is the

following: N vs. SD, D, A, SA; SD and D vs. A and SA; SD vs. D, and SA vs. A. Each contrast corresponds

to a node in the tree. In a probability tree the branches are associated with probabilities, so that the

probability of choosing a response option is the product of the probabilities of the branches needed

to reach the response option in question. In a value tree the branches are associated with values and

the value of a response option is the sum of the values of the branches needed to reach the response

option in question. The probability of choosing a response option is the value of the response option

in question divided by the sum of values of all response options.

I will explain how to build a tree, how to model the probabilities of the branches in a probability tree,

and how to model the values of the branches in a value tree. Tree models can be used to model

hypothesized processes associated with the nodes in the tree leading to a response, to model

response omissions, and to model response styles, for example the extreme response style (ERS)

which consists in preferring SD on D and SA on A. The ERS can distort test scores. The bias can be

removed using a tree model.

## (Un) Intended Consequences of a Teacher Performance Pay Program

Fecha: viernes 12 de julio de 2019

Horario: 14:00 a 15:00 hrs.

Lugar: Sala 5, Facultad de Matemáticas, Pontificia Universidad Católica de Chile**.**

Relator: Joniada Milla,Assistant Professor of Economics at Saint Mary’s University

**Abstract**:

I use a sharp regression discontinuity design (RDD) to estimate the causal e ffect of a group

pay-for-performance program in the context of secondary education. The program is long-lived and

universal in nature. The program design ensures internal and external validity of the causal e ffects

estimated, which is rare in studies that rely on RDD. By combining four Chilean administrative

datasets into a unique longitudinal data, I am able to follow all of the teachers in the system

that were a ected directly by the program and four cohorts of their students. The longitudinal

nature of the data allows me to disentangle the underlying mechanisms of the program for both

teachers and students by analyzing separately the eff ect on incumbents and switchers before and

after each round of the pay-for-performance tournament. For teachers the outcomes of interest

are mobility and third-party teacher evaluations. For students I analyze standardized test scores

that are immune to “teaching to the test” practices. I find that the eff ect of the program on

school performance operates through both sorting and incentives. The results have direct policy

implications.

Keywords: RDD, Group Performance Pay, Impact mechanisms, Test scores.