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Single Imputation from a Conditional Distribution vs Multiple Imputation for Data with a Non-monotone Missing Pattern
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0001-7282-5384
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Missing information is common in real data studies. When missingness is large, it should not be ignored and, instead, a missing data imputation method should be considered. The choice of the imputation method depends on the type or the pattern of missing information, as well as the nature of data. For instance, observations in large-scale educational assessments are incomplete by missing some components and based on usually positively correlated results within students. In all types of analysis of such data, the correlation has to be considered in a reliable calculation of properties of estimates. The aim of this paper is to compare a single imputation from a conditional distribution (with or without weights) and multiple imputation for data with a non-monotone missing pattern and high positive correlation between variables. For this purpose, such estimates as mean and variance are compared. The simulation results showed that expectation and variance are estimated more reliably when the imputation from a conditional distribution (without and with weights) or a complete-data set are used, compared to multiple imputation.

Keywords [en]
Item-nonresponse, plausible values, highly correlated measurements, large-scale assessments, planed missingness
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-128616OAI: oai:DiVA.org:umu-128616DiVA, id: diva2:1054845
Available from: 2016-12-09 Created: 2016-12-09 Last updated: 2018-06-09
In thesis
1. Statistical modeling in international large-scale assessments
Open this publication in new window or tab >>Statistical modeling in international large-scale assessments
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Statistisk modellering i internationella komparativa mätningar
Abstract [en]

This thesis contributes to the area of research based on large-scale educational assessments, focusing on the application of multilevel models. The role of sampling weights, plausible values (response variable imputed multiple times) and imputation methods are demonstrated by simulations and applications to TIMSS (Trends in International Mathematics and Science Study) and PISA (Programme for International Student Assessment) data.

The large-scale assessments use multistage sampling design, which means that the units such as schools, classrooms, or students at some or all stages are selected with unequal probabilities. In order to make valid estimates and inferences sampling weights should be used. Thus, in the first paper, we examine different approaches and give recommendations concerning handling sampling weights in multilevel models when analyzing large-scale assessments.

Due to limitations in time and the number of students, the complex surveys use matrix sampling of items. This means that a response variable, i.e. students' performance, contains a large amount of information that is missing by design. Therefore, in order to estimate students' proficiency, TIMSS and PISA use the plausible values approach, which results in a set of five plausible values – proficiencies, computed for each student. In the second paper, different user strategies concerning plausible values for multilevel models as well as means and variances are examined with both real and simulated data. Missing information that is present because of the matrix sampling design for instance like the one used in PISA, can be arranged into a non-monotone missing data pattern, where all variables are incomplete and highly positively correlated. In the third paper, we compare a few imputation methods: a single imputation from a conditional distribution (with and without weights) and multiple imputation, for data with a non-monotone missing pattern (with no complete variables) and high positive correlation between variables.

In several of the recent international large-scale assessments, students in Sweden demonstrate a decreasing performance. Some previous research has shown that changes in performance depend on students’ performance levels. In the fourth paper, we studied the relationship between student performance and the between-school variance and tried to identify factors associated with student performance in mathematics in PISA in low-, medium-, and high- performing schools in the Nordic countries.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2016. p. 18
Series
Statistical studies, ISSN 1100-8989 ; 51
Keywords
multilevel model, plausible values, sampling weights, missing information, multiple imputation, non-monotone missing pattern, TIMSS, PISA
National Category
Probability Theory and Statistics
Research subject
Statistics; Education
Identifiers
urn:nbn:se:umu:diva-128618 (URN)978-91-7601-612-1 (ISBN)
Public defence
2017-01-12, Hörsal E, Humanisthuset, Umeå Universitet, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2016-12-16 Created: 2016-12-09 Last updated: 2018-06-09Bibliographically approved

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Laukaityte, Inga

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