Biomaterial Database

Standard errors in covariance structure models: asymptotics versus bootstrap. 2006

Ke-Hai Yuan, and Kentaro Hayashi

Department of Psychology, University of Notre Dame, IN 46556, USA. kyuan@nd.edu

Commonly used formulae for standard error (SE) estimates in covariance structure analysis are derived under the assumption of a correctly specified model. In practice, a model is at best only an approximation to the real world. It is important to know whether the estimates of SEs as provided by standard software are consistent when a model is misspecified, and to understand why if not. Bootstrap procedures provide nonparametric estimates of SEs that automatically account for distribution violation. It is also necessary to know whether bootstrap estimates of SEs are consistent. This paper studies the relationship between the bootstrap estimates of SEs and those based on asymptotics. Examples are used to illustrate various versions of asymptotic variance-covariance matrices and their validity. Conditions for the consistency of the bootstrap estimates of SEs are identified and discussed. Numerical examples are provided to illustrate the relationship of different estimates of SEs and covariance matrices.

UI	MeSH Term	Description	Entries
D008297	Male		Males
D008432	Mathematical Computing	Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.	Statistical Computing,Computing, Statistical,Mathematic Computing,Statistical Programs, Computer Based,Computing, Mathematic,Computing, Mathematical,Computings, Mathematic,Computings, Mathematical,Computings, Statistical,Mathematic Computings,Mathematical Computings,Statistical Computings
D011594	Psychometrics	Assessment of psychological variables by the application of mathematical procedures.	Psychometric
D002648	Child	A person 6 to 12 years of age. An individual 2 to 5 years old is CHILD, PRESCHOOL.	Children
D003625	Data Collection	Systematic gathering of data for a particular purpose from various sources, including questionnaires, interviews, observation, existing records, and electronic devices. The process is usually preliminary to statistical analysis of the data.	Data Collection Methods,Dual Data Collection,Collection Method, Data,Collection Methods, Data,Collection, Data,Collection, Dual Data,Data Collection Method,Method, Data Collection,Methods, Data Collection
D005260	Female		Females
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000293	Adolescent	A person 13 to 18 years of age.	Adolescence,Youth,Adolescents,Adolescents, Female,Adolescents, Male,Teenagers,Teens,Adolescent, Female,Adolescent, Male,Female Adolescent,Female Adolescents,Male Adolescent,Male Adolescents,Teen,Teenager,Youths
D001077	Aptitude Tests	Primarily non-verbal tests designed to predict an individual's future learning ability or performance.	Aptitude Test,Test, Aptitude,Tests, Aptitude
D012494	Sampling Studies	Studies in which a number of subjects are selected from all subjects in a defined population. Conclusions based on sample results may be attributed only to the population sampled.	Probability Sample,Probability Samples,Sample, Probability,Samples, Probability,Sampling Study,Studies, Sampling,Study, Sampling