I am trying to model the energy content of goat milk on the basis of compositional data (e.g., protein, lactose, fat, etc..). All the data I am processing have been obtained from literature. Obviously, I have no individual data but only means. Unfortunately standard errors are not always available. So, a question arises, can I use mean values in linear regression analysis or should I perform another type of procedure to find the underlying relationship among the energy content and the other variables? Thanks in advance.
If the standard errors were always available then calculating the means and uncertainty would be very straightforward. Lacking the standard errors will make it difficult to accurately assess the uncertainty in the measurements, which is problematic but probably not fatal.
I want to make sure that I understand your data correctly. My understanding is that you have m measurements for protein content. And, for some of these measurements, l < m, you have standard errors. Then, I think there are two defensible ways to proceed with the analysis:
A.) discard the measurements without standard errors and calculate the weighted mean and standard error from the remaining data and report the results from this analysis
B.) calculate the mean and standard errors from the full set of m measurements and report the results from this analysis
C.) perform and report both a and b.
As long as you make your decision with regards to performing A,B, or C above before actually performing any of the analysis, and accurately report the procedural details, then the analysis would be acceptable. One thing you absolutely should not do is perform both A and B and report your favorite result.
Pier - Hi.
I am also not clear on the context. If you are using regression where some values are means and some are not , I think I would interpret that from something in Ken Brewer's 2002 book on survey statistics that might mean it would impact the level of heteroscedasticity. At any rate, I think heteroscedasticity should not be overlooked. Perhaps the attached might be useful.
Jim
Article Properties of Weighted Least Squares Regression for Cutoff S...
Dear James, thanks for your anwer. Probably I was not so clear as I thought. My problem is that I deal with mean compositional data coming from different papers.Only in few cases (less tha 10%) I have also the s.e. or s.d.. Thus I can't apply a meta-regressive approach. I think that my case is rather dfferent to those you anlaysed in your paper. In fact I do not deal with cutoff samples.
Hi. - Well, it does not have to have anything to do with cutoff sampling, just linear regression. Isn't your question about using these data in linear regression?
I think I misunderstood the quantity of data you had at your disposal. My answer implicity assumed that for each point (yi,xi) you have m independent estimates (yij,xij) and that for some j's you have standard errors as well. I suggested more or less that you assume the (yij,xij) are sampled from a normal distribution and that you could estimate the mean and s.d. of the distribution from the mean and s.d. of the (yij,xij)'s.
It occurs to me now that this may be a rather large data set to collect from a literature review. I am not accustomed to performing such meta-analyses (thus my overly optimistic assumption of the quantity of data available). Therefore, you shuld feel free to discount anything I have said or may say about the problem you face.
Dear Shane,
as I wrote to James, most probably I was not so clear. However I have read your answer carefully and I will capitalize it in future works. Unfortunately, not so much paper studied the problem I am interested in, and other paper reported incomplete sataset. This is a weakness of my work, but I think it is also his power. .Meanwile, I discovered some old paper dealing with regression studies performed on aggregated data (population means or rates) in contrast with the individual data analysis conterpart.. Doing so, I came across the Simpson's paradox and the the Robinson's problem of the so called "ecological fallacy" and the following discussions of thiese issuets. These papers are mainly rooted in sociology and epidemiology but they may be an useful example for me, expecially the most recent works contesting the unsuitability of aggregated data in epidemiological studies.
Pier Paolo
Metaanalysis is used for data mining and evidence based medicine reviews. This method is well described in the literature even WikipediaWikipedia
Thamks Chelyl but unfortunately no information on data variability (SD, SE) are reported throughout the dataset. I have thought to meta-regression but that lack cannot be overcome.
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