Models with ordered and unordered factors

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Models with ordered and unordered factors

Catarina Miranda
Hello;

I am having a problems with the interpretation of models using ordered or
unordered predictors.
I am running models in lmer but I will try to give a simplified example
data set using lm.
Both in the example and in my real data set I use a predictor variable
referring to 3 consecutive days of an experiment. It is a factor, and I
thought it would be more correct to consider it ordered.
Below is my example code with my comments/ideas along it.
Can someone help me to understand what is happening?

Thanks a lot in advance;

Catarina Miranda


y<-c(72,25,24,2,18,38,62,30,78,34,67,21,97,79,64,53,27,81)

Day<-c(rep("Day 1",6),rep("Day 2",6),rep("Day 3",6))

dataf<-data.frame(y,Day)

str(dataf) #Day is not ordered
#'data.frame':   18 obs. of  2 variables:
# $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
# $ Day: Factor w/ 3 levels "Day 1","Day 2",..: 1 1 1 1 1 1 2 2 2 2 ...

summary(lm(y~Day,data=dataf))  #Day 2 is not significantly different from
Day 1, but Day 3 is.
#
#Call:
#lm(formula = y ~ Day, data = dataf)
#
#Residuals:
#    Min      1Q  Median      3Q     Max
#-39.833 -14.458  -3.833  13.958  42.167
#
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)
#(Intercept)   29.833      9.755   3.058  0.00797 **
#DayDay 2      18.833     13.796   1.365  0.19234
#DayDay 3      37.000     13.796   2.682  0.01707 *
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#Residual standard error: 23.9 on 15 degrees of freedom
#Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
#F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
#

dataf$Day<-ordered(dataf$Day)

str(dataf) # "Day 1"<"Day 2"<"Day 3"
#'data.frame':   18 obs. of  2 variables:
# $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
# $ Day: Ord.factor w/ 3 levels "Day 1"<"Day 2"<..: 1 1 1 1 1 1 2 2 2 2 ...

summary(lm(y~Day,data=dataf)) #Significances reversed (or "Day.L" and
"Day.Q" are not sinonimous "Day 2" and "Day 3"?): Day 2 (".L") is
significantly different from Day 1, but Day 3 (.Q) isn't.

#Call:
#lm(formula = y ~ Day, data = dataf)
#
#Residuals:
#    Min      1Q  Median      3Q     Max
#-39.833 -14.458  -3.833  13.958  42.167
#
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)
#(Intercept)  48.4444     5.6322   8.601 3.49e-07 ***
#Day.L        26.1630     9.7553   2.682   0.0171 *
#Day.Q        -0.2722     9.7553  -0.028   0.9781
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#Residual standard error: 23.9 on 15 degrees of freedom
#Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
#F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297

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Re: Models with ordered and unordered factors

Bert Gunter
Ordered factors use orthogonal polynomial contrasts by default. The .L and
.Q stand for the linear and quadratic terms. Unordered factors use
"treatment" contrasts although (they're actually not contrasts), that are
interpreted as you described.

If you do not know what this means, you need to do some reading on linear
models/multiple regression. Try posting on   http://stats.stackexchange.com/
or, as always, consult your local statistician for help.  V&R's MASS book
also contains a useful but terse discussion on these issues.

Cheers,
Bert

On Tue, Nov 15, 2011 at 7:00 AM, Catarina Miranda <
[hidden email]> wrote:

> Hello;
>
> I am having a problems with the interpretation of models using ordered or
> unordered predictors.
> I am running models in lmer but I will try to give a simplified example
> data set using lm.
> Both in the example and in my real data set I use a predictor variable
> referring to 3 consecutive days of an experiment. It is a factor, and I
> thought it would be more correct to consider it ordered.
> Below is my example code with my comments/ideas along it.
> Can someone help me to understand what is happening?
>
> Thanks a lot in advance;
>
> Catarina Miranda
>
>
> y<-c(72,25,24,2,18,38,62,30,78,34,67,21,97,79,64,53,27,81)
>
> Day<-c(rep("Day 1",6),rep("Day 2",6),rep("Day 3",6))
>
> dataf<-data.frame(y,Day)
>
> str(dataf) #Day is not ordered
> #'data.frame':   18 obs. of  2 variables:
> # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
> # $ Day: Factor w/ 3 levels "Day 1","Day 2",..: 1 1 1 1 1 1 2 2 2 2 ...
>
> summary(lm(y~Day,data=dataf))  #Day 2 is not significantly different from
> Day 1, but Day 3 is.
> #
> #Call:
> #lm(formula = y ~ Day, data = dataf)
> #
> #Residuals:
> #    Min      1Q  Median      3Q     Max
> #-39.833 -14.458  -3.833  13.958  42.167
> #
> #Coefficients:
> #            Estimate Std. Error t value Pr(>|t|)
> #(Intercept)   29.833      9.755   3.058 0.00797 **
> #DayDay 2      18.833     13.796   1.365  0.19234
> #DayDay 3      37.000     13.796   2.682  0.01707 *
> #---
> #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #
> #Residual standard error: 23.9 on 15 degrees of freedom
> #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
> #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
> #
>
> dataf$Day<-ordered(dataf$Day)
>
> str(dataf) # "Day 1"<"Day 2"<"Day 3"
> #'data.frame':   18 obs. of  2 variables:
> # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
> # $ Day: Ord.factor w/ 3 levels "Day 1"<"Day 2"<..: 1 1 1 1 1 1 2 2 2 2 ...
>
> summary(lm(y~Day,data=dataf)) #Significances reversed (or "Day.L" and
> "Day.Q" are not sinonimous "Day 2" and "Day 3"?): Day 2 (".L") is
> significantly different from Day 1, but Day 3 (.Q) isn't.
>
> #Call:
> #lm(formula = y ~ Day, data = dataf)
> #
> #Residuals:
> #    Min      1Q  Median      3Q     Max
> #-39.833 -14.458  -3.833  13.958  42.167
> #
> #Coefficients:
> #            Estimate Std. Error t value Pr(>|t|)
> #(Intercept)  48.4444     5.6322   8.601 3.49e-07 ***
> #Day.L        26.1630     9.7553   2.682   0.0171 *
> #Day.Q        -0.2722     9.7553  -0.028   0.9781
> #---
> #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #
> #Residual standard error: 23.9 on 15 degrees of freedom
> #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
> #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
>
>        [[alternative HTML version deleted]]
>
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>

--

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm

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Re: Models with ordered and unordered factors

Bert Gunter
... In addition, the following may also be informative.

> f <- paste("day", 1:3)
> contrasts(ordered(f))
                .L         .Q
[1,] -7.071068e-01  0.4082483
[2,] -7.850462e-17 -0.8164966
[3,]  7.071068e-01  0.4082483

> contrasts(factor(f))
      day 2 day 3
day 1     0     0
day 2     1     0
day 3     0     1

Cheers,
Bert

On Tue, Nov 15, 2011 at 8:32 AM, Bert Gunter <[hidden email]> wrote:

> Ordered factors use orthogonal polynomial contrasts by default. The .L and
> .Q stand for the linear and quadratic terms. Unordered factors use
> "treatment" contrasts although (they're actually not contrasts), that are
> interpreted as you described.
>
> If you do not know what this means, you need to do some reading on linear
> models/multiple regression. Try posting on
> http://stats.stackexchange.com/  or, as always, consult your local
> statistician for help.  V&R's MASS book also contains a useful but terse
> discussion on these issues.
>
> Cheers,
> Bert
>
> On Tue, Nov 15, 2011 at 7:00 AM, Catarina Miranda <
> [hidden email]> wrote:
>
>> Hello;
>>
>> I am having a problems with the interpretation of models using ordered or
>> unordered predictors.
>> I am running models in lmer but I will try to give a simplified example
>> data set using lm.
>> Both in the example and in my real data set I use a predictor variable
>> referring to 3 consecutive days of an experiment. It is a factor, and I
>> thought it would be more correct to consider it ordered.
>> Below is my example code with my comments/ideas along it.
>> Can someone help me to understand what is happening?
>>
>> Thanks a lot in advance;
>>
>> Catarina Miranda
>>
>>
>> y<-c(72,25,24,2,18,38,62,30,78,34,67,21,97,79,64,53,27,81)
>>
>> Day<-c(rep("Day 1",6),rep("Day 2",6),rep("Day 3",6))
>>
>> dataf<-data.frame(y,Day)
>>
>> str(dataf) #Day is not ordered
>> #'data.frame':   18 obs. of  2 variables:
>> # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
>> # $ Day: Factor w/ 3 levels "Day 1","Day 2",..: 1 1 1 1 1 1 2 2 2 2 ...
>>
>> summary(lm(y~Day,data=dataf))  #Day 2 is not significantly different from
>> Day 1, but Day 3 is.
>> #
>> #Call:
>> #lm(formula = y ~ Day, data = dataf)
>> #
>> #Residuals:
>> #    Min      1Q  Median      3Q     Max
>> #-39.833 -14.458  -3.833  13.958  42.167
>> #
>> #Coefficients:
>> #            Estimate Std. Error t value Pr(>|t|)
>> #(Intercept)   29.833      9.755   3.058 0.00797 **
>> #DayDay 2      18.833     13.796   1.365  0.19234
>> #DayDay 3      37.000     13.796   2.682  0.01707 *
>> #---
>> #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>> #
>> #Residual standard error: 23.9 on 15 degrees of freedom
>> #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
>> #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
>> #
>>
>> dataf$Day<-ordered(dataf$Day)
>>
>> str(dataf) # "Day 1"<"Day 2"<"Day 3"
>> #'data.frame':   18 obs. of  2 variables:
>> # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
>> # $ Day: Ord.factor w/ 3 levels "Day 1"<"Day 2"<..: 1 1 1 1 1 1 2 2 2 2
>> ...
>>
>> summary(lm(y~Day,data=dataf)) #Significances reversed (or "Day.L" and
>> "Day.Q" are not sinonimous "Day 2" and "Day 3"?): Day 2 (".L") is
>> significantly different from Day 1, but Day 3 (.Q) isn't.
>>
>> #Call:
>> #lm(formula = y ~ Day, data = dataf)
>> #
>> #Residuals:
>> #    Min      1Q  Median      3Q     Max
>> #-39.833 -14.458  -3.833  13.958  42.167
>> #
>> #Coefficients:
>> #            Estimate Std. Error t value Pr(>|t|)
>> #(Intercept)  48.4444     5.6322   8.601 3.49e-07 ***
>> #Day.L        26.1630     9.7553   2.682   0.0171 *
>> #Day.Q        -0.2722     9.7553  -0.028   0.9781
>> #---
>> #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>> #
>> #Residual standard error: 23.9 on 15 degrees of freedom
>> #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
>> #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
>>
>>        [[alternative HTML version deleted]]
>>
>>
>> ______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>
>
> --
>
> Bert Gunter
> Genentech Nonclinical Biostatistics
>
> Internal Contact Info:
> Phone: 467-7374
> Website:
>
> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>
>
>

--

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm

        [[alternative HTML version deleted]]


______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Models with ordered and unordered factors

PaulJohnson32gmail
In reply to this post by Catarina Miranda
On Tue, Nov 15, 2011 at 9:00 AM, Catarina Miranda
<[hidden email]> wrote:

> Hello;
>
> I am having a problems with the interpretation of models using ordered or
> unordered predictors.
> I am running models in lmer but I will try to give a simplified example
> data set using lm.
> Both in the example and in my real data set I use a predictor variable
> referring to 3 consecutive days of an experiment. It is a factor, and I
> thought it would be more correct to consider it ordered.
> Below is my example code with my comments/ideas along it.
> Can someone help me to understand what is happening?

Dear Catarina:

I have had the same question, and I hope my answers help you
understand what's going on.

The short version:

http://pj.freefaculty.org/R/WorkingExamples/orderedFactor-01.R

The longer version, "Working with Ordinal Predictors"

http://pj.freefaculty.org/ResearchPapers/MidWest09/Midwest09.pdf

HTH
pj

>
> Thanks a lot in advance;
>
> Catarina Miranda
>
>
> y<-c(72,25,24,2,18,38,62,30,78,34,67,21,97,79,64,53,27,81)
>
> Day<-c(rep("Day 1",6),rep("Day 2",6),rep("Day 3",6))
>
> dataf<-data.frame(y,Day)
>
> str(dataf) #Day is not ordered
> #'data.frame':   18 obs. of  2 variables:
> # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
> # $ Day: Factor w/ 3 levels "Day 1","Day 2",..: 1 1 1 1 1 1 2 2 2 2 ...
>
> summary(lm(y~Day,data=dataf))  #Day 2 is not significantly different from
> Day 1, but Day 3 is.
> #
> #Call:
> #lm(formula = y ~ Day, data = dataf)
> #
> #Residuals:
> #    Min      1Q  Median      3Q     Max
> #-39.833 -14.458  -3.833  13.958  42.167
> #
> #Coefficients:
> #            Estimate Std. Error t value Pr(>|t|)
> #(Intercept)   29.833      9.755   3.058 0.00797 **
> #DayDay 2      18.833     13.796   1.365  0.19234
> #DayDay 3      37.000     13.796   2.682  0.01707 *
> #---
> #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #
> #Residual standard error: 23.9 on 15 degrees of freedom
> #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
> #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
> #
>
> dataf$Day<-ordered(dataf$Day)
>
> str(dataf) # "Day 1"<"Day 2"<"Day 3"
> #'data.frame':   18 obs. of  2 variables:
> # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
> # $ Day: Ord.factor w/ 3 levels "Day 1"<"Day 2"<..: 1 1 1 1 1 1 2 2 2 2 ...
>
> summary(lm(y~Day,data=dataf)) #Significances reversed (or "Day.L" and
> "Day.Q" are not sinonimous "Day 2" and "Day 3"?): Day 2 (".L") is
> significantly different from Day 1, but Day 3 (.Q) isn't.
>
> #Call:
> #lm(formula = y ~ Day, data = dataf)
> #
> #Residuals:
> #    Min      1Q  Median      3Q     Max
> #-39.833 -14.458  -3.833  13.958  42.167
> #
> #Coefficients:
> #            Estimate Std. Error t value Pr(>|t|)
> #(Intercept)  48.4444     5.6322   8.601 3.49e-07 ***
> #Day.L        26.1630     9.7553   2.682   0.0171 *
> #Day.Q        -0.2722     9.7553  -0.028   0.9781
> #---
> #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #
> #Residual standard error: 23.9 on 15 degrees of freedom
> #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
> #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
>
>        [[alternative HTML version deleted]]
>
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>



--
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas

______________________________________________
[hidden email] mailing list
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Re: Models with ordered and unordered factors

Catarina Miranda
Thanks a lot for your answers and reading suggestions, now I know my guess
was completely wrong.

I guess in my case it will be more informative to keep the unordered
factors. That way I can know not only that days differ in general, but also
get information on which day is differing from day 1.

Cheers;

Catarina


On 15 November 2011 17:54, Paul Johnson <[hidden email]> wrote:

> On Tue, Nov 15, 2011 at 9:00 AM, Catarina Miranda
> <[hidden email]> wrote:
> > Hello;
> >
> > I am having a problems with the interpretation of models using ordered or
> > unordered predictors.
> > I am running models in lmer but I will try to give a simplified example
> > data set using lm.
> > Both in the example and in my real data set I use a predictor variable
> > referring to 3 consecutive days of an experiment. It is a factor, and I
> > thought it would be more correct to consider it ordered.
> > Below is my example code with my comments/ideas along it.
> > Can someone help me to understand what is happening?
>
> Dear Catarina:
>
> I have had the same question, and I hope my answers help you
> understand what's going on.
>
> The short version:
>
> http://pj.freefaculty.org/R/WorkingExamples/orderedFactor-01.R
>
> The longer version, "Working with Ordinal Predictors"
>
> http://pj.freefaculty.org/ResearchPapers/MidWest09/Midwest09.pdf
>
> HTH
> pj
>
> >
> > Thanks a lot in advance;
> >
> > Catarina Miranda
> >
> >
> > y<-c(72,25,24,2,18,38,62,30,78,34,67,21,97,79,64,53,27,81)
> >
> > Day<-c(rep("Day 1",6),rep("Day 2",6),rep("Day 3",6))
> >
> > dataf<-data.frame(y,Day)
> >
> > str(dataf) #Day is not ordered
> > #'data.frame':   18 obs. of  2 variables:
> > # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
> > # $ Day: Factor w/ 3 levels "Day 1","Day 2",..: 1 1 1 1 1 1 2 2 2 2 ...
> >
> > summary(lm(y~Day,data=dataf))  #Day 2 is not significantly different from
> > Day 1, but Day 3 is.
> > #
> > #Call:
> > #lm(formula = y ~ Day, data = dataf)
> > #
> > #Residuals:
> > #    Min      1Q  Median      3Q     Max
> > #-39.833 -14.458  -3.833  13.958  42.167
> > #
> > #Coefficients:
> > #            Estimate Std. Error t value Pr(>|t|)
> > #(Intercept)   29.833      9.755   3.058 0.00797 **
> > #DayDay 2      18.833     13.796   1.365  0.19234
> > #DayDay 3      37.000     13.796   2.682  0.01707 *
> > #---
> > #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> > #
> > #Residual standard error: 23.9 on 15 degrees of freedom
> > #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
> > #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
> > #
> >
> > dataf$Day<-ordered(dataf$Day)
> >
> > str(dataf) # "Day 1"<"Day 2"<"Day 3"
> > #'data.frame':   18 obs. of  2 variables:
> > # $ y  : num  72 25 24 2 18 38 62 30 78 34 ...
> > # $ Day: Ord.factor w/ 3 levels "Day 1"<"Day 2"<..: 1 1 1 1 1 1 2 2 2 2
> ...
> >
> > summary(lm(y~Day,data=dataf)) #Significances reversed (or "Day.L" and
> > "Day.Q" are not sinonimous "Day 2" and "Day 3"?): Day 2 (".L") is
> > significantly different from Day 1, but Day 3 (.Q) isn't.
> >
> > #Call:
> > #lm(formula = y ~ Day, data = dataf)
> > #
> > #Residuals:
> > #    Min      1Q  Median      3Q     Max
> > #-39.833 -14.458  -3.833  13.958  42.167
> > #
> > #Coefficients:
> > #            Estimate Std. Error t value Pr(>|t|)
> > #(Intercept)  48.4444     5.6322   8.601 3.49e-07 ***
> > #Day.L        26.1630     9.7553   2.682   0.0171 *
> > #Day.Q        -0.2722     9.7553  -0.028   0.9781
> > #---
> > #Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> > #
> > #Residual standard error: 23.9 on 15 degrees of freedom
> > #Multiple R-squared: 0.3241,     Adjusted R-squared: 0.234
> > #F-statistic: 3.597 on 2 and 15 DF,  p-value: 0.05297
> >
> >        [[alternative HTML version deleted]]
> >
> >
> > ______________________________________________
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> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
> >
>
>
>
> --
> Paul E. Johnson
> Professor, Political Science
> 1541 Lilac Lane, Room 504
> University of Kansas
>
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______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.