# [R] Nestad ANOVA with random Factors

Pablo R riulp at hotmail.com
Fri Aug 27 09:43:37 CEST 2010

```Hi,

I need a help. I am new in R and I need to run a nested anova with fixed and
random factors (Mixed Model). I have a design with three factors: Day, Area
and Plot and the dependent variable is density. The factors Day and Area are
fixed while Plot is random, factor Area is nested in factor Day, and factor
Plot is nested in Area.

I can do it using aov by:

mod1<-aov(density~ day + day%in%area + day%in%area%in%plot)
symmary(mod1)

Getting this result:

Analysis of Variance Table

Response: total
Df Sum Sq Mean Sq F value  Pr(>F)
day             2 1789.8  894.91 55.5576 < 2e-16 ***
day:area       15 4658.8  310.59 19.2818 < 2e-16 ***
day:area:plot  72 1715.7   23.83  1.4793 0.01145 *
Residuals     360 5798.8   16.11
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

But I'm afraind the factor plot is not beeing calculated as random.

The other way would be using the lme from nlme as below (if I had only
factors area and plot, once I don't know how to include day and keep plot as
random) just as an exemple I found in the list files:

> mod2 <-  lme(density ~ area + plot, random = ~ 1 | area / plot, data =
> data)
> summary(mod2)

Linear mixed-effects model fit by REML
Data: data
AIC      BIC    logLik
1422.403 1475.532 -698.2017

Random effects:
Formula: ~1 | area
(Intercept)
StdDev:    0.347117

Formula: ~1 | plot %in% area
(Intercept) Residual
StdDev: 6.431067e-05 1.127295

Fixed effects: density~ area + plot
Value Std.Error  DF   t-value p-value
(Intercept)  2.6131608 0.3856554 420  6.775895  0.0000
areaarea10  -1.2073539 0.5242788   0 -2.302885     NaN
areaarea2   -0.3062031 0.5242788   0 -0.584046     NaN
areaarea4   -0.6109334 0.5242788   0 -1.165283     NaN
areaarea6   -0.9808034 0.5242788   0 -1.870767     NaN
areaarea8   -1.3437982 0.5242788   0 -2.563136     NaN
plotb       -0.0899366 0.1680473  20 -0.535187  0.5984
plotc        0.0257024 0.1680473  20  0.152947  0.8800
plotd        0.0420734 0.1680473  20  0.250366  0.8049
plote       -0.2375628 0.1680473  20 -1.413666  0.1728
Correlation:
(Intr) arer10 arear2 arear4 arear6 arear8 plotb  plotc  plotd
areaarea10 -0.680
areaarea2  -0.680  0.500
areaarea4  -0.680  0.500  0.500
areaarea6  -0.680  0.500  0.500  0.500
areaarea8  -0.680  0.500  0.500  0.500  0.500
plotb      -0.218  0.000  0.000  0.000  0.000  0.000
plotc      -0.218  0.000  0.000  0.000  0.000  0.000  0.500
plotd      -0.218  0.000  0.000  0.000  0.000  0.000  0.500  0.500
plote      -0.218  0.000  0.000  0.000  0.000  0.000  0.500  0.500  0.500

Standardized Within-Group Residuals:
Min         Q1        Med         Q3        Max
-2.3554021 -0.8985867  0.1031298  0.8008967  2.6488795

Number of Observations: 450
Number of Groups:
area plot %in% area
6             30
Warning message:
In pt(q, df, lower.tail, log.p) : NaNs produzidos

But, in addition to the lack of the factor day, I am sure its not right
because of these "NaN" produced and because of the area beeing assigned as
Random in the output.

I would appreciate any help and thanks for your attention in advance,

Pablo

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