The Experts below are selected from a list of 6099 Experts worldwide ranked by ideXlab platform
Christopher Hertzog - One of the best experts on this subject based on the ideXlab platform.
-
precision reliability and effect size of slope variance in Latent Growth Curve models implications for statistical power analysis
Frontiers in Psychology, 2018Co-Authors: Andreas M Brandmaier, Timo Von Oertzen, Ulman Lindenberger, Paolo Ghisletta, Christopher HertzogAbstract:Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the Latent intercept and its covariance with the Latent slope. We derive a new reliability index for LGCM slope variance-effective Curve reliability (ECR)-by scaling slope variance against effective error. ECR is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study's sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs.
-
precision reliability and effect size of slope variance in Latent Growth Curve models implications for statistical power analysis
Frontiers in Psychology, 2018Co-Authors: Andreas M Brandmaier, Timo Von Oertzen, Ulman Lindenberger, Paolo Ghisletta, Christopher HertzogAbstract:Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the Latent intercept and its covariance with the Latent slope. We derive a new reliability index for LGCM slope variance – effective Curve reliability (ECR) – by scaling slope variance against effective error, which is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study’s sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs.
-
Evaluating the power of Latent Growth Curve models to detect individual differences in change
Structural Equation Modeling, 2008Co-Authors: Christopher Hertzog, Timo Von Oertzen, Paolo Ghisletta, Ulman LindenbergerAbstract:We evaluated the statistical power of single-indicator Latent Growth\nCurve models to detect individual differences in change (variances\nof Latent slopes) as a function of sample size, number of longitudinal\nmeasurement occasions, and Growth Curve reliability. We recommend\nthe 2 degree-of-freedom generalized test assessing loss of fit when\nboth slope-related random effects, the slope variance and intercept-slope\ncovariance, are fixed to 0. Statistical power to detect individual\ndifferences in change is low to moderate unless the residual error\nvariance is low, sample size is large, and there are more than four\nmeasurement occasions. The generalized test has greater power than\na specific test isolating the hypothesis of zero slope variance,\nexcept when the true slope variance is close to 0, and has uniformly\nsuperior power to a Wald test based on the estimated slope variance.
-
on the power of multivariate Latent Growth Curve models to detect correlated change
Psychological Methods, 2006Co-Authors: Christopher Hertzog, Paolo Ghisletta, Ulman Lindenberger, Timo Von OertzenAbstract:We evaluated the statistical power of single-indicator Latent Growth Curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris (1985) were used to evaluate the power to detect slope covariances. Even with large samples (N = 500) and several longitudinal occasions (4 or 5), statistical power to detect covariance of slopes was moderate to low unless Growth Curve reliability at study onset was above .90. Studies using LGCMs may fail to detect slope correlations because of low power rather than a lack of relationship of change between variables. The present findings allow researchers to make more informed design decisions when planning a longitudinal study and aid in interpreting LGCM results regarding correlated interindividual differences in rates of development.
Ulman Lindenberger - One of the best experts on this subject based on the ideXlab platform.
-
precision reliability and effect size of slope variance in Latent Growth Curve models implications for statistical power analysis
Frontiers in Psychology, 2018Co-Authors: Andreas M Brandmaier, Timo Von Oertzen, Ulman Lindenberger, Paolo Ghisletta, Christopher HertzogAbstract:Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the Latent intercept and its covariance with the Latent slope. We derive a new reliability index for LGCM slope variance-effective Curve reliability (ECR)-by scaling slope variance against effective error. ECR is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study's sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs.
-
precision reliability and effect size of slope variance in Latent Growth Curve models implications for statistical power analysis
Frontiers in Psychology, 2018Co-Authors: Andreas M Brandmaier, Timo Von Oertzen, Ulman Lindenberger, Paolo Ghisletta, Christopher HertzogAbstract:Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the Latent intercept and its covariance with the Latent slope. We derive a new reliability index for LGCM slope variance – effective Curve reliability (ECR) – by scaling slope variance against effective error, which is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study’s sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs.
-
Evaluating the power of Latent Growth Curve models to detect individual differences in change
Structural Equation Modeling, 2008Co-Authors: Christopher Hertzog, Timo Von Oertzen, Paolo Ghisletta, Ulman LindenbergerAbstract:We evaluated the statistical power of single-indicator Latent Growth\nCurve models to detect individual differences in change (variances\nof Latent slopes) as a function of sample size, number of longitudinal\nmeasurement occasions, and Growth Curve reliability. We recommend\nthe 2 degree-of-freedom generalized test assessing loss of fit when\nboth slope-related random effects, the slope variance and intercept-slope\ncovariance, are fixed to 0. Statistical power to detect individual\ndifferences in change is low to moderate unless the residual error\nvariance is low, sample size is large, and there are more than four\nmeasurement occasions. The generalized test has greater power than\na specific test isolating the hypothesis of zero slope variance,\nexcept when the true slope variance is close to 0, and has uniformly\nsuperior power to a Wald test based on the estimated slope variance.
-
on the power of multivariate Latent Growth Curve models to detect correlated change
Psychological Methods, 2006Co-Authors: Christopher Hertzog, Paolo Ghisletta, Ulman Lindenberger, Timo Von OertzenAbstract:We evaluated the statistical power of single-indicator Latent Growth Curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris (1985) were used to evaluate the power to detect slope covariances. Even with large samples (N = 500) and several longitudinal occasions (4 or 5), statistical power to detect covariance of slopes was moderate to low unless Growth Curve reliability at study onset was above .90. Studies using LGCMs may fail to detect slope correlations because of low power rather than a lack of relationship of change between variables. The present findings allow researchers to make more informed design decisions when planning a longitudinal study and aid in interpreting LGCM results regarding correlated interindividual differences in rates of development.
Timo Von Oertzen - One of the best experts on this subject based on the ideXlab platform.
-
precision reliability and effect size of slope variance in Latent Growth Curve models implications for statistical power analysis
Frontiers in Psychology, 2018Co-Authors: Andreas M Brandmaier, Timo Von Oertzen, Ulman Lindenberger, Paolo Ghisletta, Christopher HertzogAbstract:Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the Latent intercept and its covariance with the Latent slope. We derive a new reliability index for LGCM slope variance-effective Curve reliability (ECR)-by scaling slope variance against effective error. ECR is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study's sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs.
-
precision reliability and effect size of slope variance in Latent Growth Curve models implications for statistical power analysis
Frontiers in Psychology, 2018Co-Authors: Andreas M Brandmaier, Timo Von Oertzen, Ulman Lindenberger, Paolo Ghisletta, Christopher HertzogAbstract:Latent Growth Curve Models (LGCM) have become a standard technique to model change over time. Prediction and explanation of inter-individual differences in change are major goals in lifespan research. The major determinants of statistical power to detect individual differences in change are the magnitude of true inter-individual differences in linear change (LGCM slope variance), design precision, alpha level, and sample size. Here, we show that design precision can be expressed as the inverse of effective error. Effective error is determined by instrument reliability and the temporal arrangement of measurement occasions. However, it also depends on another central LGCM component, the variance of the Latent intercept and its covariance with the Latent slope. We derive a new reliability index for LGCM slope variance – effective Curve reliability (ECR) – by scaling slope variance against effective error, which is interpretable as a standardized effect size index. We demonstrate how effective error, ECR, and statistical power for a likelihood ratio test of zero slope variance formally relate to each other and how they function as indices of statistical power. We also provide a computational approach to derive ECR for arbitrary intercept-slope covariance. With practical use cases, we argue for the complementary utility of the proposed indices of a study’s sensitivity to detect slope variance when making a priori longitudinal design decisions or communicating study designs.
-
Evaluating the power of Latent Growth Curve models to detect individual differences in change
Structural Equation Modeling, 2008Co-Authors: Christopher Hertzog, Timo Von Oertzen, Paolo Ghisletta, Ulman LindenbergerAbstract:We evaluated the statistical power of single-indicator Latent Growth\nCurve models to detect individual differences in change (variances\nof Latent slopes) as a function of sample size, number of longitudinal\nmeasurement occasions, and Growth Curve reliability. We recommend\nthe 2 degree-of-freedom generalized test assessing loss of fit when\nboth slope-related random effects, the slope variance and intercept-slope\ncovariance, are fixed to 0. Statistical power to detect individual\ndifferences in change is low to moderate unless the residual error\nvariance is low, sample size is large, and there are more than four\nmeasurement occasions. The generalized test has greater power than\na specific test isolating the hypothesis of zero slope variance,\nexcept when the true slope variance is close to 0, and has uniformly\nsuperior power to a Wald test based on the estimated slope variance.
-
on the power of multivariate Latent Growth Curve models to detect correlated change
Psychological Methods, 2006Co-Authors: Christopher Hertzog, Paolo Ghisletta, Ulman Lindenberger, Timo Von OertzenAbstract:We evaluated the statistical power of single-indicator Latent Growth Curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris (1985) were used to evaluate the power to detect slope covariances. Even with large samples (N = 500) and several longitudinal occasions (4 or 5), statistical power to detect covariance of slopes was moderate to low unless Growth Curve reliability at study onset was above .90. Studies using LGCMs may fail to detect slope correlations because of low power rather than a lack of relationship of change between variables. The present findings allow researchers to make more informed design decisions when planning a longitudinal study and aid in interpreting LGCM results regarding correlated interindividual differences in rates of development.
Susan C Duncan - One of the best experts on this subject based on the ideXlab platform.
-
an introduction to Latent Growth Curve modeling
Behavior Therapy, 2004Co-Authors: Terry E Duncan, Susan C DuncanAbstract:Over the past 3 decades we have witnessed an increase in the complexity of theoretical models that attempt to explain development in a number of behavioral domains. The conceptual movement to examine behavior from both developmental and contextual perspectives parallels recent methodological advances in the analysis of change. These new analysis techniques have fundamentally altered how we conceptualize and study change, and have prompted researchers to identify larger frameworks to integrate knowledge. One such framework is Latent Growth modeling. This article presents a basic Latent Growth modeling approach for analyzing repeated measures data and delineates several of its extensions, including analyses for multiple populations, accelerated designs, multivariate associative models, and a framework for sample size selection and power estimation.
-
enhancing the psychological well being of elderly individuals through tai chi exercise a Latent Growth Curve analysis
Structural Equation Modeling, 2001Co-Authors: Terry E Duncan, Susan C Duncan, Edward Mcauley, Nigel R Chaumeton, Peter HarmerAbstract:Using a randomized controlled trial, this study examined whether a Tai Chi exercise program enhanced elderly individuals' psychological well-being. Participants either continued their daily routine activities or participated in a Tai Chi exercise class performing slow rhythmic movements. Psychological well-being measures were assessed at baseline, 3 months, and 6 months (termination of the class). Latent Growth Curve modeling methodology was used to analyze the repeated measures data. Results indicated that individuals who participated in the 6-month Tai Chi exercise program showed higher levels of health perceptions, life satisfaction, positive affect, and well-being and lower levels of depression, negative affect, and psychological distress. The implications of these findings are discussed relative to potential underlying mechanisms associated with the exercise-psychological health relation in older adults.
-
Risk and protective factors influencing adolescent problem behavior: A multivariate Latent Growth Curve analysis
Annals of Behavioral Medicine, 2000Co-Authors: Susan C Duncan, Terry E Duncan, Lisa A. StryckerAbstract:This study examined the dynamic relations between adolescent problem behaviors (alcohol, marijuana, deviance, academic failure) over time and predictors of these behaviors. Data from the National Youth Survey (1) included 1,044 adolescents (53.5% male; mean age at year 1=13.20). Dependent measures were adolescent alcohol use, marijuana use, deviance, and academic failure, assessed annually over 4 years. Independent measures included age, gender, marital status, income, family time, family support, time with friends, friend deviance, knowledge of friends, activities, and neighborhood problems. An associative Latent Growth modeling (LGM) analysis showed significant increases and relations between the four behaviors in both initial status and development. Second-order multivariate LGM analyses indicated that the four behaviors could be modeled by a higher-order problem behavior construct. Significant effects on the common problem behavior intercept or slope included time with friends, deviant friends, age, marital status, family time, and support. Additional effects were found to be specific to the initial status and slopes of individual problem behaviors. Overall, results indicate the importance of assessing the relations between adolescent problem behaviors as they change over time and identifying the risk and protective factors that have both common and individual influences on these behaviors.
-
an introduction to Latent variable Growth Curve modeling concepts issues and application second edition
1999Co-Authors: Terry E Duncan, Susan C Duncan, Lisa A. StryckerAbstract:Contents: Preface. Introduction. Specification of the LGM. LGM, Repeated Measures ANOVA, and the Mixed Linear Model. Multivariate Representations of Growth and Development. Analyzing Growth in Multiple Populations. Accelerated Designs. Multilevel Longitudinal Approaches. Growth Mixture Modeling. Piecewise and Pooled Interruped Time Series LGMs. Latent Growth Curve Modeling With Categorical Variables. Missing Data Models. Latent Variable Framework for LGM Power Estimation. Testing Interaction Effects in LGMs. Summary.
-
a multivariate Latent Growth Curve analysis of adolescent substance use
Structural Equation Modeling, 1996Co-Authors: Susan C Duncan, Terry E DuncanAbstract:This article demonstrates a multivariate Latent Growth Curve methodology (LGM) for analyzing longitudinal adolescent substance use data. Hypotheses concerning the form of Growth in substance use, individual differences in the common trajectory over time, and covariates influencing Growth were tested. Significant linear increases existed for alcohol, cigarette, and marijuana use. Second‐order multivariate extensions of LGM indicated that associations among the individual differences parameters of the various substances could be adequately modeled by a higher order substance use construct. Family status, parent‐child conflict, peer encouragement for substance use, parent substance use, and age significantly influenced initial levels of use. Peer encouragement, change in peer encouragement, change in parent‐child conflict, age, and gender significantly influenced development of use. These findings support the influence of families and peers on the development of adolescent substance use and demonstrate the u...
Terry E Duncan - One of the best experts on this subject based on the ideXlab platform.
-
an introduction to Latent Growth Curve modeling
Behavior Therapy, 2004Co-Authors: Terry E Duncan, Susan C DuncanAbstract:Over the past 3 decades we have witnessed an increase in the complexity of theoretical models that attempt to explain development in a number of behavioral domains. The conceptual movement to examine behavior from both developmental and contextual perspectives parallels recent methodological advances in the analysis of change. These new analysis techniques have fundamentally altered how we conceptualize and study change, and have prompted researchers to identify larger frameworks to integrate knowledge. One such framework is Latent Growth modeling. This article presents a basic Latent Growth modeling approach for analyzing repeated measures data and delineates several of its extensions, including analyses for multiple populations, accelerated designs, multivariate associative models, and a framework for sample size selection and power estimation.
-
enhancing the psychological well being of elderly individuals through tai chi exercise a Latent Growth Curve analysis
Structural Equation Modeling, 2001Co-Authors: Terry E Duncan, Susan C Duncan, Edward Mcauley, Nigel R Chaumeton, Peter HarmerAbstract:Using a randomized controlled trial, this study examined whether a Tai Chi exercise program enhanced elderly individuals' psychological well-being. Participants either continued their daily routine activities or participated in a Tai Chi exercise class performing slow rhythmic movements. Psychological well-being measures were assessed at baseline, 3 months, and 6 months (termination of the class). Latent Growth Curve modeling methodology was used to analyze the repeated measures data. Results indicated that individuals who participated in the 6-month Tai Chi exercise program showed higher levels of health perceptions, life satisfaction, positive affect, and well-being and lower levels of depression, negative affect, and psychological distress. The implications of these findings are discussed relative to potential underlying mechanisms associated with the exercise-psychological health relation in older adults.
-
Risk and protective factors influencing adolescent problem behavior: A multivariate Latent Growth Curve analysis
Annals of Behavioral Medicine, 2000Co-Authors: Susan C Duncan, Terry E Duncan, Lisa A. StryckerAbstract:This study examined the dynamic relations between adolescent problem behaviors (alcohol, marijuana, deviance, academic failure) over time and predictors of these behaviors. Data from the National Youth Survey (1) included 1,044 adolescents (53.5% male; mean age at year 1=13.20). Dependent measures were adolescent alcohol use, marijuana use, deviance, and academic failure, assessed annually over 4 years. Independent measures included age, gender, marital status, income, family time, family support, time with friends, friend deviance, knowledge of friends, activities, and neighborhood problems. An associative Latent Growth modeling (LGM) analysis showed significant increases and relations between the four behaviors in both initial status and development. Second-order multivariate LGM analyses indicated that the four behaviors could be modeled by a higher-order problem behavior construct. Significant effects on the common problem behavior intercept or slope included time with friends, deviant friends, age, marital status, family time, and support. Additional effects were found to be specific to the initial status and slopes of individual problem behaviors. Overall, results indicate the importance of assessing the relations between adolescent problem behaviors as they change over time and identifying the risk and protective factors that have both common and individual influences on these behaviors.
-
an introduction to Latent variable Growth Curve modeling concepts issues and application second edition
1999Co-Authors: Terry E Duncan, Susan C Duncan, Lisa A. StryckerAbstract:Contents: Preface. Introduction. Specification of the LGM. LGM, Repeated Measures ANOVA, and the Mixed Linear Model. Multivariate Representations of Growth and Development. Analyzing Growth in Multiple Populations. Accelerated Designs. Multilevel Longitudinal Approaches. Growth Mixture Modeling. Piecewise and Pooled Interruped Time Series LGMs. Latent Growth Curve Modeling With Categorical Variables. Missing Data Models. Latent Variable Framework for LGM Power Estimation. Testing Interaction Effects in LGMs. Summary.
-
a multivariate Latent Growth Curve analysis of adolescent substance use
Structural Equation Modeling, 1996Co-Authors: Susan C Duncan, Terry E DuncanAbstract:This article demonstrates a multivariate Latent Growth Curve methodology (LGM) for analyzing longitudinal adolescent substance use data. Hypotheses concerning the form of Growth in substance use, individual differences in the common trajectory over time, and covariates influencing Growth were tested. Significant linear increases existed for alcohol, cigarette, and marijuana use. Second‐order multivariate extensions of LGM indicated that associations among the individual differences parameters of the various substances could be adequately modeled by a higher order substance use construct. Family status, parent‐child conflict, peer encouragement for substance use, parent substance use, and age significantly influenced initial levels of use. Peer encouragement, change in peer encouragement, change in parent‐child conflict, age, and gender significantly influenced development of use. These findings support the influence of families and peers on the development of adolescent substance use and demonstrate the u...
