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Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
Structural equation modeling (SEM) is a label for a diverse set of methods used by scientists in both experimental and observational research across the sciences, business, and other fields. It is used most in the social and behavioral sciences. A definition of SEM is difficult without reference to highly technical language, but a good starting place is the name itself.
In statistics, latent variables are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such latent variable models are used in many disciplines, including political science, demography, engineering, medicine, ecology, physics, machine learning/artificial intelligence, bioinformatics, chemometrics, natural language processing, management and the social sciences.
In statistics, the ordered logit model is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter McCullagh. For example, if one question on a survey is to be answered by a choice among "poor", "fair", "good", "very good" and "excellent", and the purpose of the analysis is to see how well that response can be predicted by the responses to other questions, some of which may be quantitative, then ordered logistic regression may be used. It can be thought of as an extension of the logistic regression model that applies to dichotomous dependent variables, allowing for more than two (ordered) response categories.
A latent variable model is a statistical model that relates a set of observable variables to a set of latent variables.
Multilevel models are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped. These models can be seen as generalizations of linear models, although they can also extend to non-linear models. These models became much more popular after sufficient computing power and software became available.
A mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same statistical units, or where measurements are made on clusters of related statistical units. Because of their advantage in dealing with missing values, mixed effects models are often preferred over more traditional approaches such as repeated measures analysis of variance.
Latent growth modeling is a statistical technique used in the structural equation modeling (SEM) framework to estimate growth trajectories. It is a longitudinal analysis technique to estimate growth over a period of time. It is widely used in the field of psychology, behavioral science, education and social science. It is also called latent growth curve analysis. The latent growth model was derived from theories of SEM. General purpose SEM software, such as OpenMx, lavaan, AMOS, Mplus, LISREL, or EQS among others may be used to estimate growth trajectories.
In statistics, a random effects model, also called a variance components model, is a statistical model where the model parameters are random variables. It is a kind of hierarchical linear model, which assumes that the data being analysed are drawn from a hierarchy of different populations whose differences relate to that hierarchy. A random effects model is a special case of a mixed model.
Joseph Michael Hilbe was an American statistician and philosopher, founding President of the International Astrostatistics Association(IAA) and one of the most prolific authors of books on statistical modeling in the early twenty-first century. Hilbe was an elected Fellow of the American Statistical Association as well as an elected member of the International Statistical Institute (ISI), for which he founded the ISI astrostatistics committee in 2009. Hilbe was also a Fellow of the Royal Statistical Society and Full Member of the American Astronomical Society.
In statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. They also inherit from GLMs the idea of extending linear mixed models to non-normal data.
In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints. Although some believe that Generalized estimating equations are robust in everything even with the wrong choice of working-correlation matrix, Generalized estimating equations are only robust to loss of consistency with the wrong choice.
Annette Jane Dobson is a Professor of Biostatistics in the University of Queensland's Centre for Longitudinal and Life Course Research (CLLR) in the School of Public Health. At her institution, she is the Head of teaching programs and a Management Executive in the Management Committee. Dobson was Director of the Australian Longitudinal Study on Women's Health from 1995 to 2013. She is a highly cited publication author, a book author, and has received an Australia Day award.
One application of multilevel modeling (MLM) is the analysis of repeated measures data. Multilevel modeling for repeated measures data is most often discussed in the context of modeling change over time ; however, it may also be used for repeated measures data in which time is not a factor.
Grace Yun Yi is a professor of the University of Western Ontario where she currently holds a Tier I Canada Research Chair in Data Science. She was a professor at the University of Waterloo, Canada, where she holds a University Research Chair in Statistical and Actuarial Science. Her research concerns event history analysis with missing data and its applications in medicine, engineering, and social science.
Quasi-variance (qv) estimates are a statistical approach that is suitable for communicating the effects of a categorical explanatory variable within a statistical model. In standard statistical models the effects of a categorical explanatory variable are assessed by comparing one category that is set as a benchmark against which all other categories are compared. The benchmark category is usually referred to as the 'reference' or 'base' category. In order for comparisons to be made the reference category is arbitrarily fixed to zero. Statistical data analysis software usually undertakes formal comparisons of whether or not each level of the categorical variable differs from the reference category. These comparisons generate the well known ‘significance values’ of parameter estimates. Whilst it is straightforward to compare any one category with the reference category, it is more difficult to formally compare two other categories of an explanatory variable with each other when neither is the reference category. This is known as the reference category problem.
In statistics, specifically regression analysis, a binary regression estimates a relationship between one or more explanatory variables and a single output binary variable. Generally the probability of the two alternatives is modeled, instead of simply outputting a single value, as in linear regression.
Andrew Richard Pickles is an English biostatistician and Professor of Biostatistics and Psychological Methods in the Institute of Psychiatry, Psychology and Neuroscience at King's College London. He was elected a Fellow of the Academy of Medical Sciences in 2009. He became a Senior Investigator at the National Institute for Health Research (NIHR) in 2018 and was elected to the British Academy in 2020.
Melanie Marie Wall is an American psychiatric biostatistician, psychometrician, and mental health data scientist who works at Columbia University as a professor in the departments of biostatistics and psychiatry, and as director of Mental Health Data Science, a joint project of the Columbia University Department of Psychiatry, Columbia University Medical Center, Research Foundation for Mental Hygiene, and New York State Psychiatric Institute. Her research has included topics such as grief and depression, eating disorders, marijuana use and abuse, and correlations between school performance and athletic activity, studied using latent variable models, spatial analysis, and longitudinal data. She is co-editor of the book Surviving Vietnam: Psychological Consequences of the War for US Veterans.
References
- 1 2 3 Curriculum vitae, retrieved 2016-07-18.
- ↑ For published book reviews, see Rabe-Hesketh's collection of links, retrieved 2016-07-18.
- ↑ ASA Honors 63 New Fellows (PDF), American Statistical Association, June 11, 2014, retrieved 2016-07-11.
