ask for help with glimmix

[Rick_SAS]

To add to sld's response, see the article "Error distributions and exponential regression models" for a discussion of log-links versus log transformed data, along with examples and pictures of the error distributions.

[jjin0322]

Thanks, Rick!

[jjin0322]

Hi sld,

Sorry for keeping bugging you two month later since my initials post.

I just had another question about my data analysis. Since the number of root tips was different in each plant, so basically the sample sizes were different for each isolate by run combination (and I am also thinking the root tips sampled from an individual plant may share more similarity than root tips sampled from different plants), I was wondering how to test if the number of root tips in an individual plant has an effect on the dependent variable (sporangia) and how to test if different plants have an effect on the dependent variable?

Hope to hear your advice. Thank you in advance!  

[sld]

I'm not entirely clear about your questions, so follow up as needed. 

If a plant is a replicate in your experiment, then the true sample size for the isolate factor is determined by the number of plants, not the number of root tips. I would agree with you that root tips are not independent, that they are clustered within plants. 

Perhaps you are wondering whether the number of root tips is affected by the isolate treatment? 

Perhaps you are wondering whether the total number of sporangia (summed over all root tips for a plant) is a better metric for sporangia production by a plant than the number of sporangia per root tip? Either metric could be justifiable, but one is likely more sensible or intuitive than the other in the biological context of the study.

If plants are replicates, then you can't assess whether different plants have an effect on the mean of the dependent variable. If you are specifically interested in these 6 plants (as opposed to thinking of them as representing "plants in general"), then it is possible to obtain a prediction (a BLUP) for each plant. I doubt that you are interested in these specific plants, but maybe you are.

HTH

[jjin0322]

Thank you for your kind reply and I really appreciated your help so far!

I guess it will be helpful to provide you more details about how I did this experiment. So I used 10ml of 10^4 zoospores/ml zoospore suspension to infect each plant (the zoospore suspensions were generated by the 2 fungal isolates that I was trying to compare their sporangia production ability around plant root tips after infection, the zoospore suspensions were adjusted to same concentration). And I left the whole root system of an individual plant in that 10ml of 10^4 zoospores/ml zoospore suspension for infection. 

My concern is that since the number of root tips of each plant is different, if a plant had a higher number of root tips, on average, each root tip was facing fewer number of zoospores during the infection process compared to a plant that had fewer root tips (So root tips from the same plant were facing same number of zoospores during infection but root tips from different plants were not facing the same number of zoospores). I am worried about if that will be a factor affecting the final number of sporangia growing around root tips from different plants. Hope I made it clear this time.

Again, thanks for your kind attention!

[sld]

This does seem like a potential concern. I think you would find it more useful to discuss this issue with colleagues who are familiar with this biological system.

There are a finite number of zoospores in the solution to which each plant is exposed. I see two possible mechanisms. (1) Even though the number of zoospores is finite, from the plant's point of view the number could effectively be infinite--in other words, there are way more zoospores than the plant can "absorb" regardless of how many root tips the plant has and each root tip is bathed in more than enough zoospores. In this case, a plant with more root tips would absorb more zoospores. (2) On the other hand, zoospore number may be limited such that a root tip on a plant with lots of root tips is "competing" with other root tips for zoospores. In this case, it might not matter how many root tips a plant has; each plant would absorb all the zoospores. (I am making these mechanisms up, and I do not attest to their validity.)

The choice of appropriate metric for sporangia production by a plant (total number of sporangia or number of sporangia per root tip) would take the mechanism of zoospore uptake and variability in number of root tips into account, as well as other aspects of this particular biological infection process. I am not knowledgeable enough about this biological system to say much more.

HTH

[jjin0322]

Yes, I absolutely agree you on the two possibilities. And based on my observation, I tend to believe possibility 1 was what happened. 

I was wondering how to test if this concern has a significant effect on sporangia production? 

I guess if I use the total number of sporangia produced by each plant for analysis, I can use the number of root tips of each plant as a covariate in the model. But what if I wanna use the  number of sporangia per root tip, could you give me some advice on how to test the potential concern in SAS program? Honestly, I have no idea how to test it in SAS.

Thank you!

[sld]

As far as getting a sense of whether the number of root tips matters, I would start with a plot of total number of sporangia (your response) versus number of root tips for each isolate, with code something like

proc sort data=<spor_plant>; by <n_root_tips>;
proc sgplot data=<spor_plant>;
  series x=<n_root_tips> y=<total_sporangia> / group=isolate;
  run;

where <spor_plant> is a dataset with one observation for each plant (aka run),

<n_root_tips> is the number of root tips for each plant, and

<total_sporangia> is the total number of sporangia, summed over all root tips, for each plant.

In this plot, do you see, for example, a trend of increasing total sporangia with increasing number of root tips? The value of this graphical assessment is limited: you have only 3 plants for each isolate and looking for trend over only 3 observations can be inconclusive. Plus you had no control over the number of root tips, so those values will fall where they fall which may not be optimal.

If you wanted to analyze the mean number of sporangia per root tip and you were using a distribution with a log link (like Poisson), you could add log(number of root tips) as an offset. Effectively, the response is the log of the ratio of total sporangia to number of root tips, i.e., the log of the number of sporangia per root tip.

See http://support.sas.com/kb/24/188.html for more detail about using an offset.

HTH

[jjin0322]

I tried to plot the data and did not see a trend of increasing total sporangia with increasing number of root tips. I guess I can not say confidently that sporangia production is not affected by the total number of root tips of an individual plant, as you mentioned, there are only 3 obervations for each isolate. 

So If I use the number of root tips of each plant as covariate in a model, and if it does not have significant effect in the model (P>0.5), can I draw the conclusion that the number of root tips of each plant does not affect sporangia production? 

For the test above (set the number of root tips of each plant as a covariate), I think I have to use the total number of sporangia of each plant, if the test result is not significant, can I jump to analyzing the data using number of sporangia on each root tip?

Also, I was wondering how can I test if there is a significant difference of sporangia production by the same isolate across different runs?

Sorry for keeping bugging you...I really appreciate your help!

[sld]

---

So If I use the number of root tips of each plant as covariate in a model, and if it does not have significant effect in the model (P>0.5), can I draw the conclusion that the number of root tips of each plant does not affect sporangia production? 

Generally speaking, you cannot draw that conclusion, especially with only 3 replications. Failure to detect significance of a factor does not mean that the factor has no effect, it just means that the study provides no evidence of an effect.

---

For the test above (set the number of root tips of each plant as a covariate), I think I have to use the total number of sporangia of each plant, if the test result is not significant, can I jump to analyzing the data using number of sporangia on each root tip?

I don't know what you mean here. Hopefully you are not thinking to use each root tip as an independent replication.

Also, I was wondering how can I test if there is a significant difference of sporangia production by the same isolate across different runs?

I refer to my response last Monday, where I said

If plants are replicates, then you can't assess whether different plants have an effect on the mean of the dependent variable. If you are specifically interested in these 6 plants (as opposed to thinking of them as representing "plants in general"), then it is possible to obtain a prediction (a BLUP) for each plant. I doubt that you are interested in these specific plants, but maybe you are.

I still doubt that the 6 plants that you used in this experiment are "special" in any way, and so I doubt that attempting to compare one plant to another is appropriate. If you disagree, describe why. Address why and how you chose these six plants to use in your experiment.

Basically, I see two analysis paths. 

(1) Analyze the effect of isolate on total sporangia production per plant. The dataset would have six observations (one for each plant), and the statistical model would be a one-way in a completely randomized design where plant is the experimental unit to which the fixed effects factor isolate is randomly assigned.

(2) Analyze the effect of isolate on sporangia production per root tip. One way to do this is to use the dataset with six observations; the response variable is total number of sporangia, assumed to follow a Poisson (or negative binomial) distribution with a log link; isolate is a fixed effects factor, and log(number of root tips) is an offset (not a covariate; an offset and a covariate are not the same thing). The statistical model is still a one-way in a completely randomized design; adding the offset results in an analysis of the effect of isolate on number of sporangia per root tip, rather than total sporangia production per plant.

You want to avoid deciding what metric to analyze based on what you see in the data. Think about why you ran this experiment, and what biological mechanism you intended to examine. If you had not yet run the experiment, what do you think would be the best response metric (total sporangia, or number of sporangia per root tip)? Your best discussion partners for this topic will be your colleagues, not me because I do not know the biological details of your system.

As a disclaimer, the opinions I've expressed here are based on my best guess of your research objectives, based on my past experience with other researchers. I may have a correct vision, or I may be totally off-track. You get to decide.

HTH