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There are several alternative ways of analyzing hierarchical data, although most of them have some problems. First, traditional statistical techniques can be used. One could disaggregate higher-order variables to the individual level, and thus conduct an analysis on this individual level (for example, assign class variables to the individual ...
Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modelled as a stochastic process.
Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. [1] The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the ...
^ = the maximized value of the likelihood function of the model , i.e. ^ = (^,), where {^} are the parameter values that maximize the likelihood function and is the observed data; n {\\displaystyle n} = the number of data points in x {\\displaystyle x} , the number of observations , or equivalently, the sample size;
Hierarchical generalized linear models are used when observations come from different clusters. There are two types of estimators: fixed effect estimators and random effect estimators, corresponding to parameters in : η = x β {\displaystyle \eta =\mathbf {x} {\boldsymbol {\beta }}} and in v ( u ) {\displaystyle \mathbf {v(u)} } , respectively.
In statistical theory, one long-established approach to higher-order statistics, for univariate and multivariate distributions is through the use of cumulants and joint cumulants. [1] In time series analysis, the extension of these is to higher order spectra, for example the bispectrum and trispectrum.
The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been obtained by Markov chain Monte Carlo (MCMC) simulation.
Bayesian structural time series (BSTS) model is a statistical technique used for feature selection, time series forecasting, nowcasting, inferring causal impact and other applications. The model is designed to work with time series data. The model has also promising application in the field of analytical marketing. In particular, it can be used ...