{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/103856"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/103856","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"How Well Can Two-Wave Models Recover the Three-Wave Second Order Latent Model Parameters?","abstract":"Although previous studies on structural equation modeling (SEM) have indicated that the second-order latent growth model (SOLGM) is a more appropriate approach to longitudinal intervention effects, its application still requires researchers to collect at least three-wave data (e.g. randomized pretest, posttest, and follow-up design). However, in some circumstances, researchers can only collect two-wave data for resource limitations. With only two-wave data, the SOLGM can not be identified and researchers often choose alternative SEM models to fit two-wave data. Recent studies show that the two-wave longitudinal common factor model (2W-LCFM) and latent change score model (2W-LCSM) can perform well for comparing latent change between groups. However, there still lacks empirical evidence about how accurately these two-wave models can estimate the group effects of latent change obtained by three-wave SOLGM (3W-SOLGM). The main purpose of this dissertation, therefore, is trying to examine to what extent the fixed effects of the tree-wave SOLGM can be recovered from the parameter estimates of the two-wave LCFM and LCSM given different simulation conditions. Fundamentally, the supplementary study (study 2) using three-wave LCFM was established to help justify the logistics of different model comparisons in our main study (study 1). The data generating model in both studies is 3W-SOLGM and there are in total 5 simulation factors (sample size, group differences in intercept and slope, the covariance between the slope and intercept, size of time-specific residual, change the pattern of time-specific residual). Three main types of evaluation indices were used to assess the quality of estimation (bias/relative bias, standard error, and power/type I error rate). The results in the supplementary study show that the performance of 3W-LCFM and 3W-LCSM are equivalent, which further justifies the different models' comparison in the main study. The point estimates for the fixed effect parameters obtained from the two-wave models are unbiased or identical to the ones from the three-wave model. However, using two-wave models could reduce the estimation precision and statistical power when the time-specific residual variance is large and changing pattern is heteroscedastic (non-constant). Finally, two real datasets were used to illustrate the simulation results.","abstract_html":"Although previous studies on structural equation modeling (SEM) have indicated that the second-order latent growth model (SOLGM) is a more appropriate approach to longitudinal intervention effects, its application still requires researchers to collect at least three-wave data (e.g. randomized pretest, posttest, and follow-up design). However, in some circumstances, researchers can only collect two-wave data for resource limitations. With only two-wave data, the SOLGM can not be identified and researchers often choose alternative SEM models to fit two-wave data. Recent studies show that the two-wave longitudinal common factor model (2W-LCFM) and latent change score model (2W-LCSM) can perform well for comparing latent change between groups. However, there still lacks empirical evidence about how accurately these two-wave models can estimate the group effects of latent change obtained by three-wave SOLGM (3W-SOLGM). The main purpose of this dissertation, therefore, is trying to examine to what extent the fixed effects of the tree-wave SOLGM can be recovered from the parameter estimates of the two-wave LCFM and LCSM given different simulation conditions. Fundamentally, the supplementary study (study 2) using three-wave LCFM was established to help justify the logistics of different model comparisons in our main study (study 1). The data generating model in both studies is 3W-SOLGM and there are in total 5 simulation factors (sample size, group differences in intercept and slope, the covariance between the slope and intercept, size of time-specific residual, change the pattern of time-specific residual). Three main types of evaluation indices were used to assess the quality of estimation (bias/relative bias, standard error, and power/type I error rate). The results in the supplementary study show that the performance of 3W-LCFM and 3W-LCSM are equivalent, which further justifies the different models' comparison in the main study. The point estimates for the fixed effect parameters obtained from the two-wave models are unbiased or identical to the ones from the three-wave model. However, using two-wave models could reduce the estimation precision and statistical power when the time-specific residual variance is large and changing pattern is heteroscedastic (non-constant). Finally, two real datasets were used to illustrate the simulation results.","abstract_has_math":false,"creators":["Du, Chenguang"],"institution":"Virginia Tech","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Educational Research and Evaluation","degree_department":"Counselor Education","school":null,"contributors":[],"advisors":[],"committee_chairs":["Miyazaki, Yasuo"],"committee_members":["Skaggs, Gary E.","Gu, Fei","Kniola, David J."],"year":2021,"date_issued":"2021-06-14","date_published":"2021-06-14","updated_at":"2026-07-22T22:19:12Z","subjects":["Latent Curve Model","Longitudinal Common Factor Model","Latent Change Score Model","Fixed Effects Parameters"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:30549"],"render_values":[{"text":"vt_gsexam:30549","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/103856","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Miyazaki, Yasuo"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Skaggs, Gary E.","Gu, Fei","Kniola, David J."]},{"key":"dc:contributor.department","label":"Department","values":["Counselor Education"]},{"key":"dc:creator","label":"Author","values":["Du, Chenguang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-06-15T08:00:25Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-06-15T08:00:25Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-06-14"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Educational Research and Evaluation"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Latent Curve Model","Longitudinal Common Factor Model","Latent Change Score Model","Fixed Effects Parameters"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:30549"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/103856"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Although previous studies on structural equation modeling (SEM) have indicated that the second-order latent growth model (SOLGM) is a more appropriate approach to longitudinal intervention effects, its application still requires researchers to collect at least three-wave data (e.g. randomized pretest, posttest, and follow-up design). However, in some circumstances, researchers can only collect two-wave data for resource limitations. With only two-wave data, the SOLGM can not be identified and researchers often choose alternative SEM models to fit two-wave data. Recent studies show that the two-wave longitudinal common factor model (2W-LCFM) and latent change score model (2W-LCSM) can perform well for comparing latent change between groups. However, there still lacks empirical evidence about how accurately these two-wave models can estimate the group effects of latent change obtained by three-wave SOLGM (3W-SOLGM). The main purpose of this dissertation, therefore, is trying to examine to what extent the fixed effects of the tree-wave SOLGM can be recovered from the parameter estimates of the two-wave LCFM and LCSM given different simulation conditions. Fundamentally, the supplementary study (study 2) using three-wave LCFM was established to help justify the logistics of different model comparisons in our main study (study 1). The data generating model in both studies is 3W-SOLGM and there are in total 5 simulation factors (sample size, group differences in intercept and slope, the covariance between the slope and intercept, size of time-specific residual, change the pattern of time-specific residual). Three main types of evaluation indices were used to assess the quality of estimation (bias/relative bias, standard error, and power/type I error rate). The results in the supplementary study show that the performance of 3W-LCFM and 3W-LCSM are equivalent, which further justifies the different models' comparison in the main study. The point estimates for the fixed effect parameters obtained from the two-wave models are unbiased or identical to the ones from the three-wave model. However, using two-wave models could reduce the estimation precision and statistical power when the time-specific residual variance is large and changing pattern is heteroscedastic (non-constant). Finally, two real datasets were used to illustrate the simulation results."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["To collect and analyze the longitudinal data is a very important approach to understand the phenomenon of development in the real world. Ideally, researchers who are interested in using a longitudinal framework would prefer collecting data at more than two points in time because it can provide a deeper understanding of the developmental processes. However, in real scenarios, data may only be collected at two-time points. With only two-wave data, the second-order latent growth model (SOLGM) could not be used. The current dissertation compared the performance of two-wave models (longitudinal common factor model and latent change score model) with the three-wave SOLGM in order to better understand how the estimation quality of two-wave models could be comparable to the tree-wave model. The results show that on average, the estimation from two-wave models is identical to the ones from the three-wave model. So in real data analysis with only one sample, the point estimate by two-wave models should be very closed to that of the three-wave model. But this estimation may not be as accurate as it is obtained by the three-wave model when the latent variable has large variability in the first or last time point. This latent variable is more likely to exist as a statelike construct in the real world. Therefore, the current study could provide a reference framework for substantial researchers who could only have access to two-wave data but are still interested in estimating the growth effect that supposed to obtain by three-wave SOLGM."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["How Well Can Two-Wave Models Recover the Three-Wave Second Order Latent Model Parameters?"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Miyazaki, Yasuo"],"dc:contributor.committeemember":["Skaggs, Gary E.","Gu, Fei","Kniola, David J."],"dc:contributor.department":["Counselor Education"],"dc:creator":["Du, Chenguang"],"dc:date.accessioned":["2021-06-15T08:00:25Z"],"dc:date.available":["2021-06-15T08:00:25Z"],"dc:date.issued":["2021-06-14"],"dc:description.abstract":["Although previous studies on structural equation modeling (SEM) have indicated that the second-order latent growth model (SOLGM) is a more appropriate approach to longitudinal intervention effects, its application still requires researchers to collect at least three-wave data (e.g. randomized pretest, posttest, and follow-up design). However, in some circumstances, researchers can only collect two-wave data for resource limitations. With only two-wave data, the SOLGM can not be identified and researchers often choose alternative SEM models to fit two-wave data. Recent studies show that the two-wave longitudinal common factor model (2W-LCFM) and latent change score model (2W-LCSM) can perform well for comparing latent change between groups. However, there still lacks empirical evidence about how accurately these two-wave models can estimate the group effects of latent change obtained by three-wave SOLGM (3W-SOLGM). The main purpose of this dissertation, therefore, is trying to examine to what extent the fixed effects of the tree-wave SOLGM can be recovered from the parameter estimates of the two-wave LCFM and LCSM given different simulation conditions. Fundamentally, the supplementary study (study 2) using three-wave LCFM was established to help justify the logistics of different model comparisons in our main study (study 1). The data generating model in both studies is 3W-SOLGM and there are in total 5 simulation factors (sample size, group differences in intercept and slope, the covariance between the slope and intercept, size of time-specific residual, change the pattern of time-specific residual). Three main types of evaluation indices were used to assess the quality of estimation (bias/relative bias, standard error, and power/type I error rate). The results in the supplementary study show that the performance of 3W-LCFM and 3W-LCSM are equivalent, which further justifies the different models' comparison in the main study. The point estimates for the fixed effect parameters obtained from the two-wave models are unbiased or identical to the ones from the three-wave model. However, using two-wave models could reduce the estimation precision and statistical power when the time-specific residual variance is large and changing pattern is heteroscedastic (non-constant). Finally, two real datasets were used to illustrate the simulation results."],"dc:description.abstractgeneral":["To collect and analyze the longitudinal data is a very important approach to understand the phenomenon of development in the real world. Ideally, researchers who are interested in using a longitudinal framework would prefer collecting data at more than two points in time because it can provide a deeper understanding of the developmental processes. However, in real scenarios, data may only be collected at two-time points. With only two-wave data, the second-order latent growth model (SOLGM) could not be used. The current dissertation compared the performance of two-wave models (longitudinal common factor model and latent change score model) with the three-wave SOLGM in order to better understand how the estimation quality of two-wave models could be comparable to the tree-wave model. The results show that on average, the estimation from two-wave models is identical to the ones from the three-wave model. So in real data analysis with only one sample, the point estimate by two-wave models should be very closed to that of the three-wave model. But this estimation may not be as accurate as it is obtained by the three-wave model when the latent variable has large variability in the first or last time point. This latent variable is more likely to exist as a statelike construct in the real world. Therefore, the current study could provide a reference framework for substantial researchers who could only have access to two-wave data but are still interested in estimating the growth effect that supposed to obtain by three-wave SOLGM."],"dc:description.degree":["Doctor of Philosophy"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:30549"],"dc:identifier.uri":["http://hdl.handle.net/10919/103856"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Latent Curve Model","Longitudinal Common Factor Model","Latent Change Score Model","Fixed Effects Parameters"],"dc:title":["How Well Can Two-Wave Models Recover the Three-Wave Second Order Latent Model Parameters?"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Educational Research and Evaluation"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:12Z"}