# Sesiones extraordinarias Seminario de Estadística Educacional 11 y 12 de julio

## 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.

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.