MANOVA | R Documentation |

This is a MANOVA rest for summarized data. This means that if we want to perform the multivariate comparison of, for example, three groups, then we can use the covariance matrices and means for the variables inside of each group to compute the statistics for a MANOVA.

```
MANOVA(
obj,
par.mat = NULL,
cov.mat = NULL,
sample.size = NULL,
groups = NULL,
boxM = TRUE
)
```

`obj` |
A list of ANOVA R objects or linear/non-linear model objects. If "obj" is not given, then the parmeters 'par.mat', 'cov.mat', and 'sample.size' must be given. |

`par.mat` |
A matrix where each column contains the model parameters of each curve. |

`cov.mat` |
List of parameter variance-covariance matrices. |

`sample.size` |
Vector with the sample sizes used to estimate each models. |

`groups` |
list of sets of indices that identify models from a same group. |

`boxM` |
Logic. Whether to perform the Box M test for covaraince matrix equality. There are two limitations associated with the Box test ([1] pag 42). First, it can be sensitive to multivariate nonnormality. Second, the degrees of freedom for this test can often be very large, resulting in an extremely sensitive/powerful test of the null hypothesis. Both of these limitations could lead a researcher to question the validity of the multivariate test on the vectors of means when the multivariate test is valid. As a result, researchers often do not rely heavily on the results of the test but rather rely on the robustness of the multivariate test on the equality of mean vectors when sample sizes are equal. |

To perform the comparison of a model under different parameter values (different curve fits with the same model), the covariance matrices and means from each set of model parameters can be used in place of the covariance matrices and means for the variables inside of each group.

If boxM = TRUE and the p-value of the test is greater than 0.05, the function will return a list with data frame as the first element carrying the statistics 'Hotelling T^2', 'Pillai's trace', 'Wilks lambda', and 'Hotelling-Lawley' trace' and the corresponding p-values. Second element will be the 'Box M' test result. If Box M' test result is not significant then the data frame with the statistics will include, in addition "Yao's F", "Johansen's F", and the "Nel-Merwe's F".

If boxM = FALSE, then the function will return a data frame with the statistics "Hotelling T^2", "Wilks lambda" and their corresponding p-values.

Robersy Sanchez (https://genomaths.com).

CARL J. HUBERTY, STEPHEN OLEJNIK.2006. Applied MANOVA and Discriminant Analysis. Second Edition. John Wiley & Sons, Inc., Hoboken, New Jersey.

Muller KE, Lavange LM, Ramey SL, Ramey CT. Power Calculations for General Linear Multivariate Models Including Repeated Measures Applications. J Am Stat Assoc. 1992;87: 1209 - 1226. doi:10.1080/01621459.1992.10476281.

Finch H, French B (2013) A Monte Carlo Comparison of Robust MANOVA Test Statistics. J Mod Appl Stat Methods 12. Available: http://digitalcommons.wayne.edu/jmasm/vol12/iss2/4.

Fouladi RT (1998) Type I Error Control of Two-Group Multivariate Tests on Means under Conditions of Heterogeneous Correlation Structure. Annual Meeting of the American Educational Research Association. San Diego, CA,. pp. 1 - 28. Available: http://files.eric.ed.gov/fulltext/ED420716.pdf.

```
## =========== Example 1 ============
library(minpack.lm)
## Build an initial random data set
set.seed(1230)
x1 <- rnorm(10000, mean = 0.5, sd = 1)
x2 <- rnorm(10000, mean = 0.6, sd = 1.2)
cdfp1 <- fitCDF(x1, distNames = 1, plot = FALSE)
cdfp2 <- fitCDF(x2, distNames = 1, plot = FALSE)
MANOVA(list(model1 = cdfp1$fit[[1]], model2 = cdfp2$fit[[1]]))
## =========== Example 2 ============
## Define a non-linear function
mutr <- function(x, alpha, beta, lambda) {
alpha / (1 + beta * exp(-lambda * x))
}
## Build two data set of points from specific curves
x1 <- sort(x1[x1 > 0]) * 10
y1 <- mutr(x1, alpha = 25, beta = 4.5, lambda = 2.1) + runif(length(x1))
y2 <- mutr(x1, alpha = 25.5, beta = 4.5,
lambda = 2.05) + runif(length(x1))
## Non-linear fit
fit1 <- nlsLM(Y ~ alpha / (1 + beta * exp(-lambda * X)),
data = data.frame(X = x1, Y = y1),
start = list(alpha = 25.5, beta = 4.5, lambda = 2.05),
control = list(
maxiter = 1024, tol = 1e-12,
minFactor = 10^-6
)
)
fit2 <- nlsLM(Y ~ alpha / (1 + beta * exp(-lambda * X)),
data = data.frame(X = x1, Y = y2),
start = list(alpha = 25, beta = 4.5, lambda = 2.1),
control = list(
maxiter = 1024, tol = 1e-12,
minFactor = 10^-6
)
)
## Manova result
MANOVA(list(model1 = fit1, model2 = fit2))
```

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