PREDICTING SCHOOL TRANSITION RATES IN AUSTRIA WITH CLASSIFICATION TREES ANNETTE M OLLER

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PREDICTING SCHOOL TRANSITION RATES IN AUSTRIA WITH

CLASSIFICATION TREES

ANNETTE M ¨

OLLER

Faculty of Business Administration and Economics, Bielefeld University, Germany

ANN CATHRICE GEORGE

Federal Institute for Quality Assurance of the Austrian School System (IQS), Austria

J¨

URGEN GROSS

Institute for Mathematics and Applied Informatics, University of Hildesheim, Germany

Abstract. Methods based on machine learning become increasingly popular in many areas

as they allow models to be ﬁtted in a highly-data driven fashion, and often show comparable

or even increased performance in comparison to classical methods. However, in the area of

educational sciences the application of machine learning is still quite uncommon. This work

investigates the beneﬁt of using classiﬁcation trees for analyzing data from educational sciences.

An application to data on school transition rates in Austria indicates diﬀerent aspects of in-

terest in the context of educational sciences: (i) the trees select variables for predicting school

transition rates in a data-driven fashion which are well in accordance with existing conﬁrmatory

theories from educational sciences, (ii) trees can be employed for performing variable selection

for regression models, (iii) the classiﬁcation performance of trees is comparable to that of binary

regression models. These results indicate that trees and possibly other machine learning meth-

ods may also be helpful to explore high-dimensional educational data sets, especially where no

conﬁrmatory theories have been developed yet.

1. Introduction

Machine learning methods become more and more popular in many applications and often

show competitive performance to traditional models from applied statistics, as e.g. regression

models. Regression and classiﬁcation trees have many appealing advantages. In contrast to

traditional regression models they can deal with very large numbers of predictors and do not

require any assumptions regarding distribution or the relationship of predictors and response.

Furthermore, a tree model is highly interpretable due to its hierarchical nature.

Although the use of machine learning is still rare in educational sciences, it recently becomes

evident that applying these methods in combination with traditional statistical methods is

helpful in many ways (Lezhnina and Kismih´ok, 2021). A few approaches utilizing machine

learning are given in the following: In Sinharay (2016) trees, random forests and boosting are

employed to predict diﬀerent variables of educational interest, as for example item diﬃculty,

E-mail addresses:annette.moeller@uni-bielefeld.de, anncathrice.george@iqs.gv.at,

juergen.gross@uni-hildesheim.de.

Key words and phrases. Regression and Classiﬁcation Trees; school transition; variable selection and im-

portance; multilevel structure of data; large-scale assessment.

This is an original manuscript of an article published by Taylor & Francis in International Journal of Research

& Method on 17 Oct 2022, available at: http://www.tandfonline.com/doi/full/10.1080/1743727X.2022.2128744.

arXiv:2210.11580v1 [stat.AP] 20 Oct 2022

2 PREDICTING SCHOOL TRANSITION RATES IN AUSTRIA WITH CLASSIFICATION TREES

high school dropouts, and scorings in electronic essays. The authors note that these methods

have slightly superior performance over traditional regression models. The work in Gao and

Rogers (2011) uses regression trees to predict and interpret item diﬃculties in a language

assessment survey and concluded that the tree structure can be used to enhance interpretation

of the items. The authors in Salles et al. (2020) made attempts to analyze data from computer

based assessments, which pose challenges to the researcher due to their high-dimensionality.

In order to continue and extend the research conducted so far in educational sciences the

issues (i) - (iii) stated in the following will be addressed in the subsequent analysis:

(i) Are the predictors selected in the tree in accordance with existing theories from educational

sciences or can even complement them (Section 4.1)?

(ii) Is it possible to utilize the variable choices of a tree as data-driven variable selection method

for building regression models to predict an educational response variable? Can such a tree-

based variable selection be supportive and complementary when choosing variables based on

educational approaches (Section 4.2)?

(iii) Is the performance of a tree comparable to the performance of traditional generalized linear

(mixed) models when applied to educational data (Section 4.3)?

In this regard classiﬁcation trees are employed to predict school transition rates in Austria

based on data of the test of educational standards in mathematics for fourth graders (BIFIE,

2019).

If the variable selection of trees indeed leads to reasonable interpretations, future research

may consider the application of trees or other machine learning methods to data and research

questions in which no educational theories exist so far. This possibility is further outlined in

Section 5.

2. Background information on data and investigated educational topic

2.1. Educational research topic and existing educational approaches. The Organiza-

tion for Cooperation and Development (OECD, 2010) has shown that unemployment rates

decrease as the level of education raises. Understanding the factors related to educational as-

piration is of great interest to educators in order to explain and predict the choices students

make during their educational paths. Students in Austria make the ﬁrst choice regarding their

educational path after grade four: for the upcoming school transition they can select between

a higher academic track, called “Allgemeine H¨ohere Schule” (AHS), which (after graduation)

allows them to enroll at a university, and lower academic tracks. Insights from educational

science show that not only the students’ competencies are of relevance for that selection but

also other social and personal factors. The present study follows the (existing) approach of

Gil-Flores et al. (2011) which model students’ aspiration in dependence of a small number of

variables they indicated in a comprehensive literature review. These variables are gender, ed-

ucational status of parents, educational attainment, socio-economic status (measured by the

number of books in the household), and parental involvement in school (measured by the stu-

dents’ equipment regarding a working place at home).

2.2. Background on data and variables. Information about students’ educational aspira-

tion, i.e. their plans which school to visit after grade four are given in the data of the Austrian

educational standard tests for fourth graders. The Austrian educational standard tests are

employed to monitor students’ competencies, and based on the results, to enhance the school

system. This study is based on data of the Austrian educational standard test in mathematics

for fourth graders in 2018 (BIFIE, 2019). The Austrian standards testing is mandatory, which

leads to a survey of 73,780 students in 4,925 classes and 2,961 schools. The present study

includes a representative sample of 8,520 students in 637 classes and 430 schools.

The data mainly includes students’ competencies in mathematics which can be categorized

into four content sub-domains (i.e. numbers, operations, measures, geometry), and four cog-

nitive sub-domains (i.e. model building, calculating, communicating, problem solving), with

PREDICTING SCHOOL TRANSITION RATES IN AUSTRIA WITH CLASSIFICATION TREES 3

Table 1. Overview on important variables in data set. The ﬁrst column contains

the variable names, the second column states the level on which a variable is

measured (in brackets the level of the corresponding aggregated variable), the

third column provides a short explanation of each variable.

Variable Data Level Description

aspiration-education student

Parents aspiration of the highest education their

children will achieve (higher values indicate

higher education)

math-grade student Grade students achieve in mathematics (higher

values indicate poorer grades)

points-calculating student

Points in the educational standards test in cog-

nitive sub-domain calculating (higher values for

higher competencies)

points-communicating student

Points in the educational standards test in cog-

nitive sub-domain communicating about math-

ematical facts (higher values for higher compe-

tencies)

private-tutoring

(private-tutoring-aggCL)

student

(class)

Number of hours for private tutoring in class

(categorized, 7 levels, higher values indicate

more hours)

after-school

(after-school-aggSL)

student

(school)

Visiting after-school supervision (higher values

indicate more time spent in supervision)

social-status

(social-status-aggSL)

student

(school)

A measure indicating the social status of the

student (higher values indicate higher social sta-

tus)

federal-state school Federal state of school location (9 states in Aus-

tria)

town-size school Size of the town where the school is located

(higher values indicate larger towns)

school-size school Total number of students attending the school

urban school

Degree of urbanization where the school is lo-

cated (higher values indicate a smaller degree of

urbanization)

each of them measured in the test (for measuring students’ competencies in all eight domains

see also Groß et al., 2016). The results are given on continuous scales with a mean value of

500.

Besides the students’ competencies additional background information of students, teachers,

parents and schools is collected via context questionnaires (BIFIE, 2018). The questionnaires

yield multifaceted information about the students’ family and school environment, as well as

personal and motivational factors. As mentioned above, the variable to be predicted in this

study is the school the students will attend in the following year.

The around 700 context variables obtained from the complete questionnaires will be employed

in the subsequent analysis to predict school transition. Table 1 presents a selection of context

variables, which will be found to be of relevance in the subsequent model building process, see,

e.g., Section 4.1.

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摘要：

PREDICTINGSCHOOLTRANSITIONRATESINAUSTRIAWITHCLASSIFICATIONTREESANNETTEMOLLERFacultyofBusinessAdministrationandEconomics,BielefeldUniversity,GermanyANNCATHRICEGEORGEFederalInstituteforQualityAssuranceoftheAustrianSchoolSystem(IQS),AustriaJURGENGROSSInstituteforMathematicsandAppliedInformatics,Unive...

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