Soil samples were taken from two locations which differ by the values of several variables (x1, x2, etc). There were N1 samples from location 1 and N2 samples from location 2. The total number of species detected in the study was K. For each (i-th) species, the number of samples in which it was found was recorded at both locations: n1 and n2, respectively. The goal is to evaluate how the probability of being found in a sample differs from location 1 to location 2 (i.e. compare n1(i)/N1 vs n2(i)/N2), and how this depends on the predictor variables x1, x2. Importantly, this should be done not only for each i-th species separately, but also for groups of species (e.g. for a given genus with several species, or for a group of species with a common property). Is logistic regression appropriate for these problems?
a multivariate logistic regression is appropriate for this data set. because your dependent variable is binary(yes or no and ...) this model applied in Various studies.in logistic regression tht type of dependent variable should be binary and this assummtion
Hi Igor
I think the logistic regression is fine, but it carries the assumption that the species have equal detection probability between the two sites. In other words that the sampling methods are equally efficient at detecting species at both of the sites. You do not say what taxa you are working with, so I have know idea if this assumption will be acceptably met, but it is worth considering either possibility.
One way to deal with variable detection between sites is to use and occupancy model. Basically, its a zero-inflated logistic regression where the zero-inflated part models the occurrence of the species and the logistic regression part models the detection process. You would model both components as random effects across species and site as a fixed effect.
You can achieve this analysis in program Presence, program Mark (model Mh), or WinBugs.
https://www.researchgate.net/profile/Kenneth_Pollock2/publication/253725909_Estimating_Species_Richness_The_Importance_of_Heterogeneity_in_Species_Detectability/links/0046353cd251eea2e1000000.pdf
But....if your sampling efficiency is equivalent between sites, logistic regression should achieve what you want.
Good luck!
Article Estimating Species Richness: The Importance of Heterogeneity...
Thank you, Adam and Dan!
The species detection probability between the two sites is probably equivalent, but independence of samples within a site may be violated. I will read the references you suggested. Meanwhile, I have the following thoughts about approaching this analysis:
1. As as initial step, compare the presence probabilities at both sites (n1(i)/N1 vs n2(i)/N2) for each species by Fisher's exact test. If no significant difference is revealed (i.e. 2 tailed p value >0.05), then a detailed logistic regression using predictor variables appears unnecessary for the given species.
2. Repeat the same test as in step 1, but for groups of species (e.g. for a particular genus). For example, for a genus with m species, one would compare SUM(n1(i), i=1..m)/(N1*m) vs SUM(n2(i), i=1..m)/(N2*m).
3. For those species or groups which show p values < 0.05 in steps 1 or 2, perform logistic regression. This assumes that samples are independent.
4. To test for effects of correlations between samples within a site, perform Monte Carlo simulation. In each simulation instance one sample at each site is randomly selected, and another randomly selected sample at each site is assigned the same value (presence or absence) for the i-th species. Logistic regression is performed on the simulated data.
I would appreciate input from anyone interested!
Hello Igor,
I found your question very relevant to one I would face in my very next work.
I agree with your step 1 of significance test to analyze the differences. The only thing I would consider before approaching the next goal is evaluating the variables effect on the species community. Hoping that you have kept your measured variables (eg. soil parameters) constant for both sites, I would advice on to first see how these affect your local population structure in time.. If their lies similarity in both sites, then possibly your logistic regression would fit best further.
Best wishes
Thank you, Manasi. I am not completely sure what you mean by "population structure in time". If you mean species composition at one location vs another, perhaps Fisher's exact test would be applicable again. It would be ued to compare proportions k1/K vs k2/K, where K is the total number of species found at both locations, k1 is the number of species found in at least one sample in location 1, and k2 is the number of species found in at least one sample in location 2. Does this make sense?
Hallo Igor,
I think the prefererable method of analysis of your data will be the Discriminant Function analysis. This computes a new variable say Z which is a linear function of variables like X1 , X2 , X3 .. etc.. This fuction can be of the type Z = a1 X1 +a2X2 +a3X3+ ......+ akXk for k variables. Z serves as a much better determinant of the two locations than does variables X1 , X2 , X3 etc. taken signly. Discriminant function helps admirably to separate the two locations based on the two or more characteristics. Thus discrimainant function analysis can be utilised for assessing the combined effect of factors that are different between the two groups of locations.
Hello Kandamuthan,
Thank you for the clarification. What is the advantage of discriminant function analysis over logistic regression in this case?
Igor
The linear discriminant function is the linear combination of the xi , ∑ai xi, which minimises the probability of misclassification. Under the assumption that the variables
X 1 , X2 , X 3........X k have a mulivariate normal distribution with differenct means for two locations, but equal covariance matrices, the coefficients βi in the logistic model can be shown to be equivalent to those of the linear discriminant function. If you come across a specimen which is unknown, you can measure the characteristics of X1 and X2 and from these, we can calculate the Z value employing previously calculated coefficients a1 and a2 and can allocate the value to the correct group.
Hi, Igor and Kandamuthan
I don't agree with Kandarmuthan comment. In many cases, the linear discriminant function is worse than the logistic regression. Especially, it is not recommended for medical diagnosis, rating and the pass/fail determination of exam scores. See my several papers published in 2014 about the comparison of the linear discriminant function, logistic regression and SVM etc.
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