I suppose you measure the photosynthesis and the nutrient conc. in several different individuals of svereal different species (the individuals used to measure the photosynthesis not neccesarily the same as those to measure the nutrients). This is actually a design with two levels of replications (species and individuals within species). The "best" approach to handle such designs is by mixed models where "species" is used as a random factor.

The "second best" approach would be to average the values within each species and simply look at the correlation between the average photosynthesis values and the average nutients values.

Caio -

I am not familiar with your subject matter and how you collect data. Are you saying you have one regressor/predictor/independent variable, and one dependent variable?  You have photosynthetic rate and some nutrient concentration value, and each are continuous data perhaps?  Which is the dependent variable?  

If you can associate one (x,y) point for each species, are you trying to compare species? Then you could plot them separately and compare slopes. 

Don't you want to treat species separately, and then compare them?

Are you saying that for any one variable, x or y, you have more than one measurement for one, for every single measurement of the other?  If so, which variable? 

If this is a one regressor problem, and you think it is linear due to your subject matter theory, you should still plot (x y) on a scatterplot to see if it looks linear. That is, are the data consistent with theory?

Is this multiple regression?

Cheers - Jim 

Hi Caio,

On which data do you calculate an average? Do you have more than one sample per species? Or do you want to calculate an average over all species?

Cheers Antonia

I suppose you measure the photosynthesis and the nutrient conc. in several different individuals of svereal different species (the individuals used to measure the photosynthesis not neccesarily the same as those to measure the nutrients). This is actually a design with two levels of replications (species and individuals within species). The "best" approach to handle such designs is by mixed models where "species" is used as a random factor.

The "second best" approach would be to average the values within each species and simply look at the correlation between the average photosynthesis values and the average nutients values.

Douglas Bates treats mixed effect modelling for diverse individuals and in longitudinal series, like  the sleepstudy in his intro to LME4. In general terms you should treat each subset apart, collect regression coeffcients and use proper stats to see if correlations are different. http://lme4.r-forge.r-project.org/lMMwR/lrgprt.pdf

James, I measured the photosynthesis and the nutrient concentrations in several different individuals of several different species (the individuals used to measure the photosynthesis not necessarily the same as those to measure the nutrients). In that example, nutrient concentration would be the predictor, independent variable and the photosynthesis would be the dependent variable (both continuous data). And Jochen was correct, I have multiple individuals for multiple species and the correlations that is important for me is for the different species. 

Antonia, I measured the photosynthesis and the nutrient concentrations in several different individuals of several different species (the individuals used to measure the photosynthesis not necessarily the same as those to measure the nutrients), so I have to calculate the average and errors for both parameters. Then I`want to use these averages and errors in a correlation based in different species. I have between 5-8 samples per species (for each parameter).

Jochen Wilhelm, I did not think about using a mixed model, and I guess that might work. To use the averages and do the correlation normally, on the other hand, does not fell right to me, as I would lose much (if not all) the variation withing each parameter throughout this process.

Caio -

Hi.

Well, when you say that "...the individuals used to measure the photosynthesis not necessarily the same as those to measure the nutrients..." I read that as a major drawback.  If I understand the averaging you are discussing, then even one data point from that averaging process, I'd say, could easily be less useful than an (x,y) from one individual plant.  Mixed effect modeling seems problematic as well, I think.

Rather than treat this as a missing value problem, perhaps you have enough data where you have both x, and y for the same individuals to do something with them, ignoring the incomplete (x,y) pairs.   And again, I suggest graphing your (complete (x,y)) points on a scatterplot or scatterplots.

If you want to compare species (and if they differ then you need to do so in some way), you have even less information.

Perhaps comparing two species might be handled simplistically as follows, from a different application, but I am not sure of your application, though this might possibly give you an idea:

 https://www.researchgate.net/publication/262143393_A_Note_on_Estimating_Impact_of_Data_Collection_Mode_Change_for_a_Given_Key_Response_Item

Best wishes - Jim 

Technical Report A Note on Estimating Impact of Data Collection Mode Change f...

Yes it is possible using regression. However you should resort to using better method such as SEM since it is developed to cater limitations in OLS.

To add to the options, I think it might be a good idea to consider the potential non-independence of species in your analysis (https://en.wikipedia.org/wiki/Phylogenetics). In some cases this might help you to increase the power of your analysis. There are several options out there to do this sort of thing, broadly classed under phylogeny comparative methods, including some phylogenetic generalized linear mixed effects models, which might be what you are after. Best of luck,

Jan

Hi Caio,

While I do not fully understand you question I have the following comments or suggestions:

You indicated that the photosynthetic data and the nutrient concentration data do come from different trees (unmatched at the tree level) but of the same species (matched at species level). It appears your only option is to correlate the mean values at the species level. I am not sure how many species you are dealing with, but the number different species is small, say less than 10, then you could potentially have a problem of a small sample. Added to that, because your data are from unmatched trees, the error could bigger thereby making any correlation that might exist – you risk accepting a wrong null hypothesis.

Suppose you collected data from many species (>30) ad that sample size is not an issue, because you are regressing averages, you are potentially violating one of the basic assumptions of linear regression, which is that the independent variable is known or measured without error. Therefore you cannot use regression in the traditional. Your option will be to use the error-in-variable regression approach. I am sure if you to a search on this you may find some simple reference on this topic. I casually remember Robert Sokal’s book titled “Biometry” gave a very elementary treatment of this topic. That may be a starting place.

Yes. When you perform linear or non-linear you will get R-square  greater than R-square for individual data.

data s;

input x y;

cards;

1  4

1  6

1  2

2  5

2  7

2  3

3  8

3 12

3 4

4  9

4  11

4  7

5  10

5  12

5  8

proc reg;

model y=x/p;

run;

data s;

input x y;

cards;

1  4

2  5

3  8

4  9

5  10

proc reg;

model y=x/p;

run;

DATA guad;

INPUT ldose response @@;

DATALINES;

-1.8367       9.3998

-1.3469       4.1491

-0.5306       -1.3535

-0.2857       -3.0114

1.102  -3.9253

1.5918 -6.7764

2.4082 -5.8774

3.3878 -3.191

4.0408 0.6672

4.5306 1.689

5.5102 4.6931

5.6735 10.2867

PROC NLIN;

PARMS c=15 b=0.4 d=0.6;

MODEL response = c + b*(ldose-d)**2;;

OUTPUT OUT=ff PREDICTED=Pff;

PROC PRINT;

RUN;

DATA guad;

INPUT ldose response @@;

DATALINES;

-1.58  6.76

-0.45  -2.1

1.13   -5

3.3     -4.4

4.25     1.5

5.5    7.4

PROC NLIN;

PARMS c=15 b=0.4 d=0.6;

MODEL response = c + b*(ldose-d)**2;;

OUTPUT OUT=ff PREDICTED=Pff;

PROC PRINT;

RUN;

Why not? Firas provided the answer: because R (or whatever you use to test the stengh of your correlation) will be (greatly) biased, especially if the underlying sub-samples or species have a large variance for the variable you are measuring through the mean. so, unless you have an idea of the within variance (the random effectJochen mentions), you do not know if the correlation is good, fair or simply spurrious.

so I'll still do it but treat the results as exploratory (id est, don't bet the farm on the F and t tests).

Based on my experience when facing similar issues in social sciences (eg, results oh households surveys in different countries) non parametric procedures may help to estimate the variance (jacknife, bootstrapping) 

Dear Caio

I woud say yes, since I have already published data with regression analysis on averaged data (per treatment) in JXB.

best regards

Andreas

Depends on what your sampling unit is. If sampling unit is the plot, for example, then you should take numerous measurements within the plot to adequately characterize the variable(s) of interest and when it comes to analyze, since the plot is your sampling unit, you would average across samples to get a plot-level data point. If individual plant is the sampling unit, then you should not average across plants.

If it can be shown that the first data collected on photosynthetic rates is a representative sample for the species surveyed, then yes, though not ideal. It’s unfortunate that you didn’t collect the nutritional data concurrently, especially if you want to find out if there is going to be a correlation. However, if you don’t know that there is a relationship between rates (dep. varb?) and concentration (indep. varb?), then no. If you do know that there is a relationship and just want to demonstrate the strength of the correlation, then absolutely.

Dear Dr. Caio,

As a teacher, my first opinion is to guide you to understand what kind of data you have or still having collecting. Asking for help, you first typed the word “IF”. Thus, I figure out that you have a problem about EDA (Exploratory data analysis). In the question, it seems you are investigating an area where some different species of plants have responses under study. In this case, typing DATAPLOT on Google you can understand the three methods of data analysis, beginning with EDA application. Applying EDA, you started studying variation instead the effects of treatments which you did not report in your question. It does not matter if you have data for species A and B, just cluster their names in the first column in the Excel, and the responses in the next. Next, you can apply a box-and-whiskers plots (at least five, six data – it seems you have many more) or a scatter plot as suggested by Dr. James Knaub. Finishing the EDA, you can calculate the probability of response based on several statistical distribution suggested by the EDA graphical system. Furthermore, a little bit harsh work that you can make it easy if your research team do not have a statistician. Well, we have available for free in the internet a software named VTFIT. This software has several statistical distributions which allow us to complement the results from the EDA. The disadvantage is that it run in the DOS system, but it seems that all the current computers have this system still working. My new one has it. In my page in the Researchgate you can find the reference with the manual. Finally, I did not fit only the means, never, because this method is a good way to hide variation. The coefficient of determination is increased, of course. Based on your information, I hope you can appreciate the above considerations.

Yours Sincerely

Walter

If averaging raw data to produce processed data for smoothing by linear regression, then it may be helpful to check first the range occupied by the raw data samples.  Are they drawn from the same process and measured by the same method?  If not then they may  fall into different ranges.   In any case, the method of averaging becomes at issue. For example, I have found that the geomean often produces better results in cases of processing very diverse data.  You refer to collecting "data on nutrient concentration for the same species" but ask yourself:  Is the method of collection a variable or is there any other variable that can affect the range of the samples?  If so, select the appropriate averaging technique.

I previously noted that "If I understand the averaging you are discussing, then even one data point from that averaging process, I'd say, could easily be less useful thIan an (x,y) from one individual plant."

We casn assume that previous reviews about nutrition and photosynthesis have got ground. http://www.jstor.org/stable/2097327?seq=1#page_scan_tab_contents; If this holds the use of averages instead of individual data deprecates mixed models and looks for a simplified relationshpi that has been overlooked. The homogeneity of variance and the corraction for natural fertility are often misleading. A shade plant with slow growth rate can have an optimal photosynthesis at very low imputs and the question is how to compare it with tall trees that reach deep horizons or maize that reqires strong imputs with C4 apparatuses. As fara Statistics behindI think the reference of Doug Bates is the right framework http://lme4.r-forge.r-project.org/lMMwR/lrgprt.pdf......

following

Yes, it is possible, concerning the main question of the discussion thread.

Regards

Of course, the approval (or not) of the results, using either averaged data or individual data points, is another subject matter.

Caio,

What will be most helpful to you is the research on methods of meta-analysis. Im medicine, especially, there is a great deal of work done in combining what is referred to as individual patient data (IPD) and the results from other studies. Ecology also has a strand of research on the topic. The parameter of focus is typically an effect size—including correlations. Borenstein and associates (2009) provide an excellent introduction.

Best,

Ken

Possible yes, but its quite outdated with the emergence of Structural Equation Modeling

Since the set/sample of individuals from which data on photosynthetic rate have been collected is different from the set/sample of individuals from which data on nutrient concentration have been collected therefore linear regression analysis is not applicable in this case. For the validity of regression analysis, each pair of observations on the two variables namely photosynthetic rate and nutrient concentration must be taken from the same individual.

Yes it is very very possible

Dear Dr. Caio,

Your question is very interesting and important.

I totally agree with the answer of Dr. Chakrabarty. Actually, he has explained clearly the reason for the difficulty of achieving a linear regression with averaged data instead of individual data points in your data set.

Interestingly, the other scholars have provided a potential possibility to analyze your data with some other statistical methods according to the arguments that they mentioned in their answers.

Therefore, it would be very helpful if you inform us what was the final decision in analyzing your data regarding your question to learn how to deal correctly with the same problem in case of a researcher have the same problem.

Please if you have published your paper with these data sets, provide us with the pdf. of your paper.

With kind and best regards,

Heba

First, even though it may be possible to use averaged data, why not using individual data? Second: are you sure your results are linearly related? Computers now offer more sophisticated types of regression (exponential, logarithmic, hyperbolic, polynomial...) that may be closer to a mechanistically-significant relationship.

@ R.E. Ita

The answer given by R.E. Ita needs to be explained more for better understanding.

@ Heba Elsalahy ,

I am of the same view as that of yours. With kind and best regards, Dhritikesh Chakrabarty

I would say there is some mess within the answers. Somenof them obviate the point that individuals with measures of one variable don't have measures with the ither variable. This precludes some of the proposed techniques, such as SEM or working at the individual level.

Generally, I would say "Yes, you can". But you need to think carefully what is you're question. You can estimate a regression among species of X on Y, but that does not repond the sane question as a regression among individuals of X on Y. So, maybe you're not getting the answer you were looking for...or matbe that is just what you wanted. But don't mess both levels of analysis: one of them is interspecific and the other intraspecific.

Of course, you can use a mixed model, but beware that individual would be nested within species in a non-balanced design...and as you don't have X and Y for the same individal you'll get a interspecific regression of X on Y...that is it will estimate the regression among specific means. The result should be the same as calculatingvrhe means and carrying out the regrssion, but you would use more efficiently your information (by using it to estimate the uncertainty of each specific mean)...and it's much more complex to fit.

Sorry for the long response. As a set aside, most often means do have, actually, better properties than the original variables (central theorem of the limit).

There is no statistical problem with that regression, then, you just need to understand what it means.

Hioe that helps.

Good luck!!