[R] How to test a difference in ratios of count data in R

[Greg Snow]

It is usually best to keep these discussions on the list.  Someone
else may have a better answer than mine, or be able to respond
quicker, and if I answer on R-help then it is community
service/involvement.  If I respond directly then it is consulting and
then we need a contract and I have to charge you (not that I would see
the money myself, but it would help my budget be a little less red).

For your question, your fit4 and my fit2 are just 2 different ways of
fitting the exact same model to the exact same data, so there is no
surprise that the results match.  Which one to use is personal
preference.

The line that starts with "treatmentB" is the coefficient
(log-odds-ratio) for B compared to A, so that is the main line to look
at for interpretation.

The correlation of the fixed effects is mainly there for diagnostics,
if it is too close to -1 or 1 then that indicates that assumptions may
not hold, or computations may be in doubt.  Your value is not of
concern.


On Wed, Sep 28, 2016 at 2:14 PM, Shuhua Zhan <szhan at uoguelph.ca> wrote:
> Hi Greg,
> Thank you very much for your help!
> I'd like to use glmer. From the output of summary(fit2) as below, Could I
> draw a conclusion that the treatment B
> significantly increases the counts of x group (p=6.11e-07)? I'm wondering if
> I could know that the treatment B
> significantly increases the ratio of x group (X/n) and how I could obtain
> the mean ratios of treatment A and B.
> To this end, should I fit the model using the ratio of X group (X/n)?  I
> tried it as
> fit4 <- glmer( X/n ~ treatment + (1|replicate), data=test, family=binomial,
> weights=n)
> but summary(fit4) is the same as summary(fit2).
> I also don't know how to interpret "Correlation of Fixed Effects: treatmentB
> -0.568 in the output.
>> summary(fit2)
> Generalized linear mixed model fit by maximum likelihood (Laplace
>   Approximation) [glmerMod]
>  Family: binomial  ( logit )
> Formula: cbind(X, n - X) ~ treatment + (1 | replicate)
>    Data: test
>
>      AIC      BIC   logLik deviance df.resid
>     30.1     29.4    -12.0     24.1        3
>
> Scaled residuals:
>      Min       1Q   Median       3Q      Max
> -0.88757 -0.35065 -0.03137  0.26897  0.67505
>
> Random effects:
>  Groups    Name        Variance Std.Dev.
>  replicate (Intercept) 0.4123   0.6421
> Number of obs: 6, groups:  replicate, 3
>
> Fixed effects:
>             Estimate Std. Error z value Pr(>|z|)
> (Intercept)  -1.7442     0.5438  -3.208  0.00134 **
> treatmentB    2.3647     0.4741   4.988 6.11e-07 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
>            (Intr)
> treatmentB -0.568
>
> Thanks again,
> Joshua
>
> ________________________________
> From: Greg Snow <538280 at gmail.com>
> Sent: Wednesday, September 28, 2016 12:49:49 PM
> To: Shuhua Zhan
> Cc: r-help at R-project.org
> Subject: Re: [R] How to test a difference in ratios of count data in R
>
> There are multiple ways of doing this, but here are a couple.
>
> To just test the fixed effect of treatment you can use the glm function:
>
> test <- read.table(text="
> replicate treatment n X
> 1 A 32 4
> 1 B 33 18
> 2 A 20 6
> 2 B 21 18
> 3 A 7 0
> 3 B 8 4
> ", header=TRUE)
>
> fit1 <- glm( cbind(X,n-X) ~ treatment, data=test, family=binomial)
> summary(fit1)
>
> Note that the default baseline value may differ between R and SAS,
> which would result in a reversed sign on the slope coefficient (and
> different intercept).
>
> To include replicate as a random effect you need an additional
> package, here I use lme4 and the glmer function:
>
> library(lme4)
> fit2 <- glmer( cbind(X, n-X) ~ treatment + (1|replicate), data=test,
> family=binomial)
> summary(fit2)
>
>
>
> On Tue, Sep 27, 2016 at 9:03 PM, Shuhua Zhan <szhan at uoguelph.ca> wrote:
>> Hello R-experts,
>> I am interested to determine if the ratio of counts from two groups differ
>> across two distinct treatments. For example, we have three replicates of
>> treatment A, and three replicates of treatment B. For each treatment, we
>> have counts X from one group and counts Y from another group. My
>> understanding is that that GLIMMIX procedure in SAS can calculate whether
>> the ratio of counts in one group (X/X+Y) significantly differs between
>> treatments.
>>
>> I think this is the way you do it in SAS. The replicate and treatment
>> variables are self-explanatory. The first number (n) refers to the total
>> counts X + Y; the second number (X) refers to the counts X. Is there a way
>> to do this in R? Since we have 20,000 datasets to be tested, it may be
>> easier to retrive the significant test as the given dataset below and its
>> p>F value and mean ratios of treatments in R than SAS.
>>
>>
>> data test;
>> input replicate treatment$ n X;
>> datalines;
>> 1 A 32 4
>> 1 B 33 18
>> 2 A 20 6
>> 2 B 21 18
>> 3 A 7 0
>> 3 B 8 4
>> ;
>>
>> proc glimmix data=test;
>> class replicate treatment;
>> model X/n = treatment / solution;
>> random intercept / subject=replicate;
>> run;
>>
>> ods select lsmeans;
>> proc glimmix data=test;
>> class replicate treatment;
>> model X/n = treatment / solution;
>> random intercept / subject=replicate;
>> lsmeans treatment / cl ilink;
>> run;
>>
>> I appreciate your help in advance!
>> Joshua
>>
>>
>>         [[alternative HTML version deleted]]
>>
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>
>
>
> --
> Gregory (Greg) L. Snow Ph.D.
> 538280 at gmail.com



-- 
Gregory (Greg) L. Snow Ph.D.
538280 at gmail.com