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  2. Bayesian hierarchical modeling - Wikipedia

    en.wikipedia.org/wiki/Bayesian_hierarchical_modeling

    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 ...

  3. Multilevel model - Wikipedia

    en.wikipedia.org/wiki/Multilevel_model

    Another way to analyze hierarchical data would be through a random-coefficients model. This model assumes that each group has a different regression model—with its own intercept and slope. [5] Because groups are sampled, the model assumes that the intercepts and slopes are also randomly sampled from a population of group intercepts and slopes.

  4. Marginal model - Wikipedia

    en.wikipedia.org/wiki/Marginal_model

    In a typical multilevel model, there are level 1 & 2 residuals (R and U variables). The two variables form a joint distribution for the response variable ().In a marginal model, we collapse over the level 1 & 2 residuals and thus marginalize (see also conditional probability) the joint distribution into a univariate normal distribution.

  5. Empirical Bayes method - Wikipedia

    en.wikipedia.org/wiki/Empirical_Bayes_method

    Empirical Bayes methods can be seen as an approximation to a fully Bayesian treatment of a hierarchical Bayes model.. In, for example, a two-stage hierarchical Bayes model, observed data = {,, …,} are assumed to be generated from an unobserved set of parameters = {,, …,} according to a probability distribution ().

  6. Fixed effects model - Wikipedia

    en.wikipedia.org/wiki/Fixed_effects_model

    In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are random variables.

  7. Multilevel regression with poststratification - Wikipedia

    en.wikipedia.org/wiki/Multilevel_regression_with...

    The multilevel regression is the use of a multilevel model to smooth noisy estimates in the cells with too little data by using overall or nearby averages. One application is estimating preferences in sub-regions (e.g., states, individual constituencies) based on individual-level survey data gathered at other levels of aggregation (e.g ...

  8. Seemingly unrelated regressions - Wikipedia

    en.wikipedia.org/.../Seemingly_unrelated_regressions

    In econometrics, the seemingly unrelated regressions (SUR) [1]: 306 [2]: 279 [3]: 332 or seemingly unrelated regression equations (SURE) [4] [5]: 2 model, proposed by Arnold Zellner in (1962), is a generalization of a linear regression model that consists of several regression equations, each having its own dependent variable and potentially ...

  9. Bivariate analysis - Wikipedia

    en.wikipedia.org/wiki/Bivariate_analysis

    The least squares regression line is a method in simple linear regression for modeling the linear relationship between two variables, and it serves as a tool for making predictions based on new values of the independent variable. The calculation is based on the method of the least squares criterion. The goal is to minimize the sum of the ...

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