Variance Components and Mixed Model ANOVA/ANCOVA. is a specialized module for designs with random
effects and/or factors with many levels; options for handling random effects and for estimating
variance components are also provided in the General Linear Models module. Random effects (factors)
occur frequently in industrial research, when the levels of a factor represent values sampled from
a random variable (as opposed to being deliberately chosen or arranged by the experimenter). The
Variance Components module will allow you to analyze designs with any combinations of fixed effects,
random effects, and covariates.
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Extremely large ANOVA/ANCOVA designs can be efficiently analyzed:
Factors can have several hundreds of levels. The program will analyze standard factorial (crossed)
designs as well as hierarchically nested designs, and compute the standard Type I, II, and III
analysis of variance sums of squares and mean squares for the effects in the model. In addition,
you can compute the table of expected mean squares for the effects in the design, the variance
components for the random effects in the model, the coefficients for the denominator synthesis,
and the complete ANOVA table with tests based on synthesized error sums of squares and degrees
of freedom (using Satterthwaite's method). Other methods for estimating variance components are
also supported (e.g., MIVQUE0, Maximum Likelihood [ML], Restricted Maximum Likelihood [REML]).
For maximum likelihood estimation, both the Newton-Raphson and Fisher scoring algorithms are used,
and the model will not be arbitrarily changed (reduced) during estimation to handle situations
where most components are at or near zero. Several options for reviewing the weighted and
unweighted marginal means, and their confidence intervals, are also available. Extensive graphics
options can be used to visualize the results.
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This module features a comprehensive implementation of a variety of techniques for analyzing
censored data from social, biological, and medical research, as well as procedures used in
engineering and marketing (e.g., quality control, reliability estimation, etc.). In addition
to computing life tables with various descriptive statistics and Kaplan-Meier product limit
estimates, the user can compare the survivorship functions in different groups using a large
selection of methods (including the Gehan test, Cox F-test, Cox-Mantel test, Log-rank test,
and Peto & Peto generalized Wilcoxon test).
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Also, Kaplan-Meier plots can be computed for groups
(uncensored observations are identified in graphs with different point markers). The program
also features a selection of survival function fitting procedures (including the Exponential,
Linear Hazard, Gompertz, and Weibull functions) based on either unweighted and weighted least
squares methods (maximum-likelihood parameter estimates for various distributions, including
Weibull, can also be computed via the STATISTICA Process Analysis module). Finally, the program
offers full implementations of four general explanatory models (Cox's proportional hazard model,
exponential regression model, log-normal and normal regression models) with extended diagnostics,
including stratified analysis and graphs of survival for user-specified values of predictors.
For Cox proportional hazard regression, the user can choose to stratify the sample to permit
different baseline hazards in different strata (but a constant coefficient vector), or the user
can allow for different baseline hazards as well as coefficient vectors. In addition, general
facilities are provided to define one or more time-dependent covariates. Time-dependent covariates
can be specified via a flexible formula interpreter that allows the user to define the covariates
via arithmetic expressions which may include time, as well as the standard logical functions
(e.g., timdep=age+age*log(t_)*(age>45), where t_ references survival time) and a wide variety
of distribution functions. As in all other modules of STATISTICA, the user can access and change
the technical parameters of all procedures (or accept dynamic defaults). The module also offers
an extensive selection of graphics and specialized diagrams to aid in the interpretation of
results (including plots of cumulative proportions surviving/failing, patterns of censored data,
hazard and cumulative hazard functions, probability density functions, group comparison plots,
distribution fitting plots, various residual plots, and many others).
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