Dear Ecolog-gers One question has been bothered me for a while is to calculate a change point and its confidence intervals. We have used a conditional probability analysis to determine the probability of impairment, so the response variable is probability of impairment when an ecological attribute is less than certain value (e.g, native taxa<10), the predictor is a stressor gradient (e.g. chemical concentrations). In a peer reviewed paper, a deviance reduction approach was used to detect change point in the conditional probability analysis.
I am particularly interested in using change point analysis to determine the threshold. However, several questions have bothered me and I hope you will have some insights on the analysis. 1. What is the underlying assumption for a deviance reduction analysis? The conditional probability (CP) is calculated based on a binomial distribution (impaired or not) and the response variable CP is basically a cumulative frequency of sample points. Therefore, each point of the response variable (CP) is not independent. Does that violate any assumption of independence for deviance reduction? 2. Also a chi-square test for deviance reduction significance test was proposed in Venables and Ripley (2002) book. Is the test applicable for the CP-stressor relationship? A bootstrapping technique was also proposed to calculate the CI of the change point for the CP? DO you think it makes sense when the y-axis is a discrete or binomial variable? SO THE REAL QUESTION is: ARE SIGNIFICANCE TEST AND BOOTSTRAPING CI APPLICABLE FOR CHANGE POINT IN A CONDITIONAL PROBABILITY~STRESSOR RELATIOSHIOP? Thanks, Lei
