Add the most important recent advances in multivariate statistical methods to your core PRIMER 8 toolkit. Handle complex multi-factor designs, hierarchical models and random/mixed effects with ease.
Permutational multivariate (or univariate) analysis of variance (PERMANOVA) allows you to partition variation in your high-dimensional data in response to complex multi-factor experimental/sampling designs on the basis of a chosen resemblance measure. Construct the correct pseudo F-statistic and obtain rigorous P-values using robust permutation algorithms for each term in the model given the full design, including fixed or random factors, hierarchical designs, covariates and so much more. Incorporating major new changes in version 8, such as allowing for heterogeneous dispersions and the option to include factors drawn from finite populations, PERMANOVA in PRIMER is the only software that successfully achieves all of this, and with just a few clicks.
Follow up your PERMANOVA analysis with suitable pairwise comparisons that are built to cope rigorously with the framework of your full experimental / sampling design. Get rigorous Monte Carlo estimated P-values when there are too few permutations available to achieve a useful test. Build your own contrasts to compare particular levels or sets of levels of factors. PERMANOVA puts you in the driver’s seat to build a correct and appropriate analysis to match your specific hypotheses.
Ordinations of raw data can be messy and uninformative. This is simply because residual (small-scale) variation is typically quite high. Use centroid plots of main effects and/or interaction cells to generate an informative birds-eye view of the most important factors in your study and how they might interact.
Test the null hypothesis of no differences in multivariate dispersion (beta diversity) among groups based on a chosen resemblance measure. Provide a factor identifying the groups to be compared, choose to obtain p-values from tables or using permutation of residuals and specify the number of permutations. Optionally output pair-wise tests as well, or individual deviation values of sample units to their own group centroid (and/or their means) to a worksheet for subsequent plotting.
Fit a linear model (multivariate multiple regression) on the basis of a resemblance measure of choice (DISTLM). Specify the predictor variables to be included in the model and the ordering of the fit, or perform model selection by choosing a selection procedure (forward, backward, step-wise, or ‘best’) and a selection criterion (R^2, Adjusted R^2, AIC, AICc, or BIC). Do marginal tests or sequential conditional tests, with p-values obtained using permutation of residuals under a reduced model. Check out a dbRDA plot associated with the final model fit.
Dissimilarity-based redundancy analysis (dbRDA) produces ordination axes to show the fitted variation from a DISTLM. Show the predictor variables as vectors on the dbRDA ordination. Achieve a classical RDA by doing dbRDA on the basis of a Euclidean distance matrix.
Canonical analysis of principal coordinates (CAP) finds linear combinations of unit-scaled PCO axes from a resemblance matrix that: (i) best discriminate groups (provided as a factor), (ii) best discriminate positions along a single gradient, or (iii) correlate best with linear combinations of some other set of variables. Calculate leave-one-out cross-validation/ residual SS for the CAP model. Optionally add new samples and predict their positions on CAP axes / group membership / gradient position. Optionally do a permutation test and/or output CAP scores to a worksheet, including predicted values/classifications for new samples. When based on a Euclidean distance measure, the CAP method corresponds to classical discriminant analysis (for groups) or canonical correlation analysis (for gradients), but with all tests by robust permutation.
Implement a dissimilarity-based multivariate control chart. Discern if a new sample point (e.g., in a monitoring context) is ‘in-control’ or ‘out-of-control’, by comparison with a reference set of previous (‘in-control’) observations. Choose the number of initial control-chart samples and the type of chart (progressive, fixed baseline or moving window). Specify the alpha-level and type of upper control-chart limit (non-parametric or parametric). Robust non-parametric limits are obtained from quantiles of a permutation distribution. Choose to apply shrinkage for high-dimensional systems.
