Biomaterial Database

Markov regression models for time series: a quasi-likelihood approach. 1988

S L Zeger, and B Qaqish

Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205.

This paper discusses a quasi-likelihood (QL) approach to regression analysis with time series data. We consider a class of Markov models, referred to by Cox (1981, Scandinavian Journal of Statistics 8, 93-115) as "observation-driven" models in which the conditional means and variances given the past are explicit functions of past outcomes. The class includes autoregressive and Markov chain models for continuous and categorical observations as well as models for counts (e.g., Poisson) and continuous outcomes with constant coefficient of variation (e.g., gamma). We focus on Poisson and gamma data for illustration. Analogous to QL for independent observations, large-sample properties of the regression coefficients depend only on correct specification of the first conditional moment.

UI	MeSH Term	Description	Entries
D008390	Markov Chains	A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.	Markov Process,Markov Chain,Chain, Markov,Chains, Markov,Markov Processes,Process, Markov,Processes, Markov
D009044	Motor Cortex	Area of the FRONTAL LOBE concerned with primary motor control located in the dorsal PRECENTRAL GYRUS immediately anterior to the central sulcus. It is comprised of three areas: the primary motor cortex located on the anterior paracentral lobule on the medial surface of the brain; the premotor cortex located anterior to the primary motor cortex; and the supplementary motor area located on the midline surface of the hemisphere anterior to the primary motor cortex.	Brodmann Area 4,Brodmann Area 6,Brodmann's Area 4,Brodmann's Area 6,Premotor Cortex and Supplementary Motor Cortex,Premotor and Supplementary Motor Cortices,Anterior Central Gyrus,Gyrus Precentralis,Motor Area,Motor Strip,Precentral Gyrus,Precentral Motor Area,Precentral Motor Cortex,Premotor Area,Premotor Cortex,Primary Motor Area,Primary Motor Cortex,Secondary Motor Areas,Secondary Motor Cortex,Somatic Motor Areas,Somatomotor Areas,Supplementary Motor Area,Area 4, Brodmann,Area 4, Brodmann's,Area 6, Brodmann,Area 6, Brodmann's,Area, Motor,Area, Precentral Motor,Area, Premotor,Area, Primary Motor,Area, Secondary Motor,Area, Somatic Motor,Area, Somatomotor,Area, Supplementary Motor,Brodmann's Area 6s,Brodmanns Area 4,Brodmanns Area 6,Central Gyrus, Anterior,Cortex, Motor,Cortex, Precentral Motor,Cortex, Premotor,Cortex, Primary Motor,Cortex, Secondary Motor,Cortices, Secondary Motor,Gyrus, Anterior Central,Gyrus, Precentral,Motor Area, Precentral,Motor Area, Primary,Motor Area, Secondary,Motor Area, Somatic,Motor Areas,Motor Cortex, Precentral,Motor Cortex, Primary,Motor Cortex, Secondary,Motor Strips,Precentral Motor Areas,Precentral Motor Cortices,Premotor Areas,Primary Motor Areas,Primary Motor Cortices,Secondary Motor Area,Secondary Motor Cortices,Somatic Motor Area,Somatomotor Area,Supplementary Motor Areas
D011336	Probability	The study of chance processes or the relative frequency characterizing a chance process.	Probabilities
D012044	Regression Analysis	Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.	Regression Diagnostics,Statistical Regression,Analysis, Regression,Analyses, Regression,Diagnostics, Regression,Regression Analyses,Regression, Statistical,Regressions, Statistical,Statistical Regressions
D000200	Action Potentials	Abrupt changes in the membrane potential that sweep along the CELL MEMBRANE of excitable cells in response to excitation stimuli.	Spike Potentials,Nerve Impulses,Action Potential,Impulse, Nerve,Impulses, Nerve,Nerve Impulse,Potential, Action,Potential, Spike,Potentials, Action,Potentials, Spike,Spike Potential
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D000882	Haplorhini	A suborder of PRIMATES consisting of six families: CEBIDAE (some New World monkeys), ATELIDAE (some New World monkeys), CERCOPITHECIDAE (Old World monkeys), HYLOBATIDAE (gibbons and siamangs), CALLITRICHINAE (marmosets and tamarins), and HOMINIDAE (humans and great apes).	Anthropoidea,Monkeys,Anthropoids,Monkey
D013997	Time Factors	Elements of limited time intervals, contributing to particular results or situations.	Time Series,Factor, Time,Time Factor
D015233	Models, Statistical	Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.	Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model