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This is the aim of multiple factor analysis which balances the different issues (i.e. the different groups of variables) within a global analysis and provides, beyond the classical results of factorial analysis (mainly graphics of individuals and of categories), several results (indicators and graphics) specific of the group structure.
Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery". A stated confidence level generally applies only to each test considered individually, but often it is desirable to have a confidence level for the whole family of simultaneous tests. [ 4 ]
with y i denoting the i th response in the data set and x i the vector of explanatory variables, each set at the corresponding values found in the i th observation in the data set. If the model fit to the data were correct, the residuals would approximate the random errors that make the relationship between the explanatory variables and the ...
The independent or explanatory variable (say X) can be split up into classes or segments and linear regression can be performed per segment. Segmented regression with confidence analysis may yield the result that the dependent or response variable (say Y) behaves differently in the various segments. [3]
Some extensions of response surface methodology deal with the multiple response problem. Multiple response variables create difficulty because what is optimal for one response may not be optimal for other responses. Other extensions are used to reduce variability in a single response while targeting a specific value, or attaining a near maximum ...
Example of direct replication and conceptual replication. There are two main types of replication in statistics. First, there is a type called “exact replication” (also called "direct replication"), which involves repeating the study as closely as possible to the original to see whether the original results can be precisely reproduced. [3]
GPR is a Bayesian non-linear regression method. A Gaussian process (GP) is a collection of random variables, any finite number of which have a joint Gaussian (normal) distribution. A GP is defined by a mean function and a covariance function, which specify the mean vectors and covariance matrices for each finite collection of the random variables.
The M in M-estimation stands for "maximum likelihood type". The method is robust to outliers in the response variable, but turned out not to be resistant to outliers in the explanatory variables (leverage points). In fact, when there are outliers in the explanatory variables, the method has no advantage over least squares.