[R] suggestion for optimal plotting to show significant differences

[Richard M. Heiberger]

Petr,

My first attempt is to use the simple=TRUE argument to interaction2wt.

Then the bwplots in the item|item panel show the behavior of value over day
for each item.  You get a plot similar to this panel with the growth curve plots
from nlme, for example,
    bwplot(value ~ day | item, data=test, horizontal=FALSE)
I am treating set as a replication and each box is cumulated over the
three sets.

My analysis question is about day.  You have it as numeric.  My
inclination would
be to make day factor.  Then you could model the interaction of day and item.

Rich

On Mon, Feb 9, 2015 at 6:01 AM, PIKAL Petr <petr.pikal at precheza.cz> wrote:
> Hallo Richard.
>
> I tried your suggestion but it seems to be no better than simple ggplot. Let me extend the example a bit to 8 items which is more realistic.
>
> item<-rep(letters[1:8], each=18)
> day<-rep((0:5)*100, 24)
> set<-rep(rep(1:3, each=6), 8)
> test<-data.frame(item, day, set)
> set.seed(111)
> test$value<-(test$day/100+1)+rnorm(144)
> test$value<-test$value+(as.numeric(test$item)*1.3)
>
> Value is increasing during time (day) for each tested subject (item), each item is measured 3 times (set) each day.
>
> Here is some graph
> p<-ggplot(test, aes(x=day, y=value, colour=item))
> p+geom_point()+stat_smooth(method="lm", formula= y~poly(x,2))
>
> I can do lm or aov, however I am not sure about proper formula.
>
> fit<-lm(value~day, data=test)
> summary(fit)
> # this shows that value is increasing with day
>
> fit<-lm(value~day/item, data=test)
> summary(fit)
> # this suggests that value is decreasing with day (which is wrong)
>
> fit<-lm(value~day*item, data=test)
> summary(fit)
> # and this tells me that value is increasing with day and items have different intercepts but the same rate of growth (I hope I got it right).
>
> I do not have your book available but I went through help pages.
>
> Your interaction graph is not much better than ggplot.
> I can do
>
> interaction2wt(value ~ item * day, data=test)
>
> which probably is closer to actual problem.
>
> The basic problem is that increase of value with days is in fact not linear and actually it can increase in the beginning and then stagnate or it can stagnate in beginning and then increase. I am not aware of any way how to compare time behaviour of different items in such situations if I cannot state some common formula in which case I would use probably nlme.
>
> Thank for your insight, I try to go through it more deeply.
>
> Best regards
> Petr
>
>
>> -----Original Message-----
>> From: Richard M. Heiberger [mailto:rmh at temple.edu]
>> Sent: Friday, February 06, 2015 6:14 PM
>> To: PIKAL Petr
>> Cc: r-help at r-project.org
>> Subject: Re: [R] suggestion for optimal plotting to show significant
>> differences
>>
>> I would try one of these illustrations for starts.
>> interaction2wt (two-way tables) is designed to be used with aov() for
>> testing.
>> interaction2wt shows all main effects and all two-way interactions for
>> many factors.
>>
>>
>>
>> test <-
>> structure(list(item = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
>> 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("A", "B"), class =
>> "factor"), day = c(0L, 100L, 200L, 300L, 400L, 500L, 0L, 100L, 200L,
>> 300L, 400L, 500L, 0L, 100L, 200L, 300L, 400L, 500L, 0L, 100L, 200L,
>> 300L, 400L, 500L, 0L, 100L, 200L, 300L, 400L, 500L, 0L, 100L, 200L,
>> 300L, 400L, 500L), set = c(1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
>> 2L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
>> 2L, 3L, 3L, 3L, 3L, 3L, 3L), value = c(1.08163365169503,
>> 2.61998412608805, 3.07820466606394, 4.44993419381934, 5.29163171545805,
>> 6.29155990999293, -0.123163011367676, 2.07767236834003,
>> 2.32537052874901, 3.09372794501084, 6.65273721166635, 5.92304962329131,
>> 1.50504697705548, 2.66253728086866, 2.63420157418685, 2.78195098580416,
>> 6.47578642973288, 5.89587443775143, 0.848864231485078,
>> 1.27549677119713, 2.19573089053609, 2.45659926134292, 5.15424403414103,
>> 5.4813151140983, 1.25731482647214, 2.09662105167973, 1.75954023316977,
>> 4.81624002288939, 4.65029189325307, 6.39946904227214,
>> 0.944996929887344, 1.74667265331284, 2.42956264345558,
>> 5.17852980415141, 3.5453435965834, 6.9011238437191)), .Names =
>> c("item", "day", "set", "value"), row.names = c(NA, -36L), class =
>> "data.frame")
>>
>>
>>
>> library(HH)
>>
>> test$set <- factor(test$set)
>> test$day <- factor(test$day)
>> test$item <- factor(test$item)
>>
>> interaction2wt(value ~ item * day * set, data=test)
>>
>> test$item.day <- interaction(test$item, test$day)
>> position(test$item.day) <- outer(c(-10,10),
>> as.numeric(levels(test$day)), `+`)
>>
>> xyplot(value ~ as.position(item.day) | set, groups=item,
>>         data=test, horizontal=FALSE, pch=c(17,16),
>>         xlab="day",
>>         scales=list(
>>           x=list(
>>             alternating=1,
>>             at=levels(test$day), ## placement of tick labels and marks
>>             tck=1)),
>>         key=list(
>>           text=list(c("A","B"), col=c("blue","red")),
>>           points=list(pch=c(17, 16), col=c("blue","red")),
>>        space="top", columns=2, border=TRUE),
>>        layout=c(3,1))
>>
>>
>> ## see also the examples in
>> demo(package="HH", bwplot.examples)
>>
>> On Fri, Feb 6, 2015 at 6:09 AM, PIKAL Petr <petr.pikal at precheza.cz>
>> wrote:
>> > Dear all
>> >
>> > I would like to ask for your opinion about possible graphical
>> representation of such data.
>> >
>> >> dput(test)
>> > structure(list(item = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>> > 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
>> > 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("A", "B"), class
>> =
>> > "factor"), day = c(0L, 100L, 200L, 300L, 400L, 500L, 0L, 100L, 200L,
>> > 300L, 400L, 500L, 0L, 100L, 200L, 300L, 400L, 500L, 0L, 100L, 200L,
>> > 300L, 400L, 500L, 0L, 100L, 200L, 300L, 400L, 500L, 0L, 100L, 200L,
>> > 300L, 400L, 500L), set = c(1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
>> 2L,
>> > 2L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
>> > 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L), value = c(1.08163365169503,
>> > 2.61998412608805, 3.07820466606394, 4.44993419381934,
>> > 5.29163171545805, 6.29155990999293, -0.123163011367676,
>> > 2.07767236834003, 2.32537052874901, 3.09372794501084,
>> > 6.65273721166635, 5.92304962329131, 1.50504697705548,
>> > 2.66253728086866, 2.63420157418685, 2.78195098580416,
>> > 6.47578642973288, 5.89587443775143, 0.848864231485078,
>> > 1.27549677119713, 2.19573089053609, 2.45659926134292,
>> > 5.15424403414103, 5.4813151140983, 1.25731482647214,
>> 2.09662105167973,
>> > 1.75954023316977, 4.81624002288939, 4.65029189325307,
>> > 6.39946904227214, 0.944996929887344, 1.74667265331284,
>> > 2.42956264345558, 5.17852980415141, 3.5453435965834,
>> > 6.9011238437191)), .Names = c("item", "day", "set", "value"),
>> > row.names = c(NA, -36L), class = "data.frame")
>> >>
>> >
>> > One option I came with is
>> >
>> > library(ggplot2)
>> > p<-ggplot(test, aes(x=day, y=value, colour=item))
>> > p+geom_point()+stat_smooth(method="lm", formula= y~poly(x,2))
>> >
>> > but -
>> > I have more items (around 5-10), and I want to show if the difference
>> between items is or is not significant. The actual development of value
>> with day is usually not linear nor growing steadily and actually I
>> cannot usually evaluate some analytical equation for my data to compare
>> equation parameters.
>> >
>> > I thought about boxplots, but there is not many repetitions and
>> actually 5+ boxplots can be quite messy.
>> >
>> > I can plot only mean for each set and item but in that case I lose
>> information if the difference is or is not significant.
>> >
>> > I appreciate any suggestion.
>> >
>> > Best regards
>> > Petr
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
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> Tento e-mail a jakékoliv k němu připojené dokumenty jsou důvěrné a jsou určeny pouze jeho adresátům.
> Jestliže jste obdržel(a) tento e-mail omylem, informujte laskavě neprodleně jeho odesílatele. Obsah tohoto emailu i s přílohami a jeho kopie vymažte ze svého systému.
> Nejste-li zamýšleným adresátem tohoto emailu, nejste oprávněni tento email jakkoliv užívat, rozšiřovat, kopírovat či zveřejňovat.
> Odesílatel e-mailu neodpovídá za eventuální škodu způsobenou modifikacemi či zpožděním přenosu e-mailu.
>
> V případě, že je tento e-mail součástí obchodního jednání:
> - vyhrazuje si odesílatel právo ukončit kdykoliv jednání o uzavření smlouvy, a to z jakéhokoliv důvodu i bez uvedení důvodu.
> - a obsahuje-li nabídku, je adresát oprávněn nabídku bezodkladně přijmout; Odesílatel tohoto e-mailu (nabídky) vylučuje přijetí nabídky ze strany příjemce s dodatkem či odchylkou.
> - trvá odesílatel na tom, že příslušná smlouva je uzavřena teprve výslovným dosažením shody na všech jejích náležitostech.
> - odesílatel tohoto emailu informuje, že není oprávněn uzavírat za společnost žádné smlouvy s výjimkou případů, kdy k tomu byl písemně zmocněn nebo písemně pověřen a takové pověření nebo plná moc byly adresátovi tohoto emailu případně osobě, kterou adresát zastupuje, předloženy nebo jejich existence je adresátovi či osobě jím zastoupené známá.
>
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> If you received this e-mail by mistake, please immediately inform its sender. Delete the contents of this e-mail with all attachments and its copies from your system.
> If you are not the intended recipient of this e-mail, you are not authorized to use, disseminate, copy or disclose this e-mail in any manner.
> The sender of this e-mail shall not be liable for any possible damage caused by modifications of the e-mail or by delay with transfer of the email.
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