Performs multivariate analysis of variance on PCA objects.
Usage
MANOVA(x, fac, test = "Hotelling", retain, drop)
# S3 method for OpnCoe
MANOVA(x, fac, test = "Hotelling", retain, drop)
# S3 method for OutCoe
MANOVA(x, fac, test = "Hotelling", retain, drop)
# S3 method for PCA
MANOVA(x, fac, test = "Hotelling", retain = 0.99, drop)Arguments
- x
a Coe object
- fac
a name of a colum in the
$facslot, or its id, or a formula- test
a test for manova (
'Hotelling'by default)- retain
how many harmonics (or polynomials) to retain, for PCA the highest number of PC axis to retain, or the proportion of the variance to capture.
- drop
how many harmonics (or polynomials) to drop
Details
Performs a MANOVA/MANCOVA on PC scores. Just a wrapper around manova. See examples for multifactorial manova and summary.manova for more details and examples.
Note
Needs a review and should be considered as experimental.
Silent message and progress bars (if any) with options("verbose"=FALSE).
Examples
# MANOVA
bot.p <- PCA(efourier(bot, 12))
#> 'norm=TRUE' is used and this may be troublesome. See ?efourier #Details
MANOVA(bot.p, 'type')
#> PC axes 1 to 7 were retained
#> Df Hotelling-Lawley approx F num Df den Df Pr(>F)
#> fac 1 2.7631 12.631 7 32 1.202e-07 ***
#> Residuals 38
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
op <- PCA(npoly(olea, 5))
#> 'nb.pts' missing and set to: 91
MANOVA(op, 'domes')
#> PC axes 1 to 2 were retained
#> Df Hotelling-Lawley approx F num Df den Df Pr(>F)
#> fac 1 0.37378 38.686 2 207 5.315e-15 ***
#> Residuals 208
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
m <- manova(op$x[, 1:5] ~ op$fac$domes * op$fac$var)
summary(m)
#> Df Pillai approx F num Df den Df Pr(>F)
#> op$fac$domes 1 0.38594 25.3915 5 202 < 2.2e-16 ***
#> op$fac$var 2 0.34192 8.3723 10 406 2.069e-12 ***
#> Residuals 206
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
summary.aov(m)
#> Response PC1 :
#> Df Sum Sq Mean Sq F value Pr(>F)
#> op$fac$domes 1 11.79 11.790 1.2623 0.26251
#> op$fac$var 2 109.81 54.903 5.8784 0.00329 **
#> Residuals 206 1924.02 9.340
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Response PC2 :
#> Df Sum Sq Mean Sq F value Pr(>F)
#> op$fac$domes 1 62.486 62.486 93.511 < 2.2e-16 ***
#> op$fac$var 2 34.489 17.244 25.806 9.97e-11 ***
#> Residuals 206 137.654 0.668
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Response PC3 :
#> Df Sum Sq Mean Sq F value Pr(>F)
#> op$fac$domes 1 0.2345 0.234541 3.9476 0.04826 *
#> op$fac$var 2 0.5998 0.299918 5.0479 0.00724 **
#> Residuals 206 12.2393 0.059414
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Response PC4 :
#> Df Sum Sq Mean Sq F value Pr(>F)
#> op$fac$domes 1 0.12558 0.125582 8.5246 0.003894 **
#> op$fac$var 2 0.08698 0.043490 2.9521 0.054442 .
#> Residuals 206 3.03476 0.014732
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Response PC5 :
#> Df Sum Sq Mean Sq F value Pr(>F)
#> op$fac$domes 1 0.000140 0.00014009 0.7838 0.3770
#> op$fac$var 2 0.000299 0.00014964 0.8372 0.4344
#> Residuals 206 0.036819 0.00017873
#>
# MANCOVA example
# we create a numeric variable, based on centroid size
bot %<>% mutate(cs=coo_centsize(.))
# same pipe
bot %>% efourier %>% PCA %>% MANOVA("cs")
#> 'norm=TRUE' is used and this may be troublesome. See ?efourier #Details
#> 'nb.h' set to 10 (99% harmonic power)
#> PC axes 1 to 7 were retained
#> Df Hotelling-Lawley approx F num Df den Df Pr(>F)
#> fac 1 0.38135 1.7433 7 32 0.1341
#> Residuals 38