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A Monte Carlo simulation to examine the effects of violating the normality assumption in 2-level hierarchical linear models with unbalanced designs.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	A Monte Carlo simulation to examine the effects of violating the normality assumption in 2-level hierarchical linear models with unbalanced designs./
Author:	Ketelsen, Kirk L.
Description:	1 online resource (144 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 76-05, Section: B.
Contained By:	Dissertations Abstracts International76-05B.
Subject:	Statistics. -
Online resource:	click for full text (PQDT)
ISBN:	9781321321951

A Monte Carlo simulation to examine the effects of violating the normality assumption in 2-level hierarchical linear models with unbalanced designs.
Ketelsen, Kirk L.

A Monte Carlo simulation to examine the effects of violating the normality assumption in 2-level hierarchical linear models with unbalanced designs. - 1 online resource (144 pages)

Source: Dissertations Abstracts International, Volume: 76-05, Section: B.

Thesis (Ph.D.)--University of Northern Colorado, 2014.

Includes bibliographical references

Hierarchical Linear Modeling (HLM) is emerging as a preferred method for analyzing nested data when a hierarchical data structure exists. The purpose of this dissertation was to examine the performance of HLM under varying conditions commonly found in educational research. A Monte Carlo simulation was conducted to examine how varying levels of level-1 imbalance, intraclass correlation coefficients level-2 sample size, and non-normal level-2 error distribution would affect the fixed parameter estimates and their standard errors, type I error rates, and power. The HLM performed best when level-2 sample size was large, ICC was small, and level-2 error distribution was normal. Overall, fixed parameter estimates remained accurate under all conditions, however, standard errors were over-inflated when the level-2 error distribution was highly skewed (chi-squared). Power was acceptable for most design conditions except when the ICC was very large (.25). Implications for applied researchers include how to optimally design their studies (large level-2 sample size) to have sufficient power, as well as for checking for potential type II errors when level-2 error distribution is skewed.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9781321321951Subjects--Topical Terms:

556824
Statistics.
Subjects--Index Terms:

Hierarchical linear modelingIndex Terms--Genre/Form:

554714
Electronic books.

A Monte Carlo simulation to examine the effects of violating the normality assumption in 2-level hierarchical linear models with unbalanced designs.
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504 $a Includes bibliographical references
520 $a Hierarchical Linear Modeling (HLM) is emerging as a preferred method for analyzing nested data when a hierarchical data structure exists. The purpose of this dissertation was to examine the performance of HLM under varying conditions commonly found in educational research. A Monte Carlo simulation was conducted to examine how varying levels of level-1 imbalance, intraclass correlation coefficients level-2 sample size, and non-normal level-2 error distribution would affect the fixed parameter estimates and their standard errors, type I error rates, and power. The HLM performed best when level-2 sample size was large, ICC was small, and level-2 error distribution was normal. Overall, fixed parameter estimates remained accurate under all conditions, however, standard errors were over-inflated when the level-2 error distribution was highly skewed (chi-squared). Power was acceptable for most design conditions except when the ICC was very large (.25). Implications for applied researchers include how to optimally design their studies (large level-2 sample size) to have sufficient power, as well as for checking for potential type II errors when level-2 error distribution is skewed.
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