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PARAMETRIC AND NON PARAMETRIC (MARS: MULTIVARIATE ADDITIVE REGRESSION SPLINES) LOGISTIC REGRESSIONS FOR PREDICTION OF A DICHOTOMOUS RESPONSE VARIABLE WITH AN EXAMPLE FOR PRESENCE/ABSENCE OF AMPHIBIANS
Citation:
Nash, M S. AND D F. Bradford. PARAMETRIC AND NON PARAMETRIC (MARS: MULTIVARIATE ADDITIVE REGRESSION SPLINES) LOGISTIC REGRESSIONS FOR PREDICTION OF A DICHOTOMOUS RESPONSE VARIABLE WITH AN EXAMPLE FOR PRESENCE/ABSENCE OF AMPHIBIANS. U.S. Environmental Protection Agency, Washington, DC, EPA/600/R-01/081 (NTIS PB2002-102297), 2001.
Impact/Purpose:
The primary objectives of this research are to:
Develop methodologies so that landscape indicator values generated from different sensors on different dates (but in the same areas) are comparable; differences in metric values result from landscape changes and not differences in the sensors;
Quantify relationships between landscape metrics generated from wall-to-wall spatial data and (1) specific parameters related to water resource conditions in different environmental settings across the US, including but not limited to nutrients, sediment, and benthic communities, and (2) multi-species habitat suitability;
Develop and validate multivariate models based on quantification studies;
Develop GIS/model assessment protocols and tools to characterize risk of nutrient and sediment TMDL exceedence;
Complete an initial draft (potentially web based) of a national landscape condition assessment.
This research directly supports long-term goals established in ORDs multiyear plans related to GPRA Goal 2 (Water) and GPRA Goal 4 (Healthy Communities and Ecosystems), although funding for this task comes from Goal 4. Relative to the GRPA Goal 2 multiyear plan, this research is intended to "provide tools to assess and diagnose impairment in aquatic systems and the sources of associated stressors." Relative to the Goal 4 Multiyear Plan this research is intended to (1) provide states and tribes with an ability to assess the condition of waterbodies in a scientifically defensible and representative way, while allowing for aggregation and assessment of trends at multiple scales, (2) assist Federal, State and Local managers in diagnosing the probable cause and forecasting future conditions in a scientifically defensible manner to protect and restore ecosystems, and (3) provide Federal, State and Local managers with a scientifically defensible way to assess current and future ecological conditions, and probable causes of impairments, and a way to evaluate alternative future management scenarios.
Description:
The purpose of this report is to provide a reference manual that could be used by investigators for making informed use of logistic regression using two methods (standard logistic regression and MARS). The details for analyses of relationships between a dependent binary response variable (e.g., presence/absence) and a set of independent variables are provided step by step for use by scientists who are not statisticians. Details of such statistical analyses and their assumptions are often omitted from published literature, yet such details are essential to the proper conduct of statistical analyses and interpretation of results. In this report, we use a data set for amphibian presence/absence and associated habitat variables as an example.
Relationships between a response variable and independent variable(s) are commonly quantified and described by regression models. The values of the coefficients and predictions from the fitted model are used to infer and describe patterns of relationships, the effect of the independent variables on the response, and the strength of association between the independent and response variable. All these will help to analyze and understand a phenomena, in this case biological phenomena. The general linear model (GLM) offers a wide range of regression models where the simple regression, analyses of covariance, and ANOVA are special cases. In GLM, the functional relationships between the expected value of the response variable(s) and the independent variables are described via a link function as: