Modeling the Past: A Note on the Search for Proper Form

As historians move beyond the computation of predictive measures to fashion regression models of past behavior they need to consider not only the estimation of regression parameters, but also the specification of a functional form for the model itself. The choice of a particular form for expressing the relationships among variables often has important implications for interpreting the historical issues under investigation. This paper presents methodology developed by J. B. Ramsey and other theorists for comparing distinct functional forms of a regression model according to criteria other than differences in the capacity to account for variation in the dependent variable. Ramsey's procedure directly tests the hypothesis of correctly specified functional form through scrutiny of the pattern of residuals that would be expected for properly specified models. The methodology can thus provide useful information on the choice of computing models especially when measures of explained variation are too close in value to indicate a clear preference for a given equation

Modeling the Past: A Note on the Search for Proper Form

As historians move beyond the computation of predictive measures to fashion regression models of past behavior they need to consider not only the estimation of regression parameters, but also the specification of a functional form for the model itself. The choice of a particular form for expressing the relationships among variables often has important implications for interpreting the historical issues under investigation. This paper presents methodology developed by J. B. Ramsey and other theorists for comparing distinct functional forms of a regression model according to criteria other than differences in the capacity to account for variation in the dependent variable. Ramsey's procedure directly tests the hypothesis of correctly specified functional form through scrutiny of the pattern of residuals that would be expected for properly specified models. The methodology can thus provide useful information on the choice of computing models especially when measures of explained variation are too close in value to indicate a clear preference for a given equation

Phytoplankton-Specific Response to Enrichment of Phosphorus-Rich Surface Waters with Ammonium, Nitrate, and Urea

<div><p>Supply of anthropogenic nitrogen (N) to the biosphere has tripled since 1960; however, little is known of how <em>in situ</em> response to N fertilisation differs among phytoplankton, whether species response varies with the chemical form of N, or how interpretation of N effects is influenced by the method of analysis (microscopy, pigment biomarkers). To address these issues, we conducted two 21-day <em>in situ</em> mesocosm (3140 L) experiments to quantify the species- and genus-specific responses of phytoplankton to fertilisation of P-rich lake waters with ammonium (NH₄⁺), nitrate (NO₃⁻), and urea ([NH₂]₂CO). Phytoplankton abundance was estimated using both microscopic enumeration of cell densities and high performance liquid chromatographic (HPLC) analysis of algal pigments. We found that total algal biomass increased 200% and 350% following fertilisation with NO₃⁻ and chemically-reduced N (NH₄⁺, urea), respectively, although 144 individual taxa exhibited distinctive responses to N, including compound-specific stimulation (<em>Planktothrix agardhii</em> and NH₄⁺), increased biomass with chemically-reduced N alone (<em>Scenedesmus</em> spp., <em>Coelastrum astroideum</em>) and no response (<em>Aphanizomenon flos-aquae</em>, <em>Ceratium hirundinella</em>). Principle components analyses (PCA) captured 53.2–69.9% of variation in experimental assemblages irrespective of the degree of taxonomic resolution of analysis. PCA of species-level data revealed that congeneric taxa exhibited common responses to fertilisation regimes (e.g., <em>Microcystis aeruginosa</em>, <em>M</em>. <em>flos-aquae</em>, <em>M</em>. <em>botrys</em>), whereas genera within the same division had widely divergent responses to added N (e.g., <em>Anabaena</em>, <em>Planktothrix</em>, <em>Microcystis</em>). Least-squares regression analysis demonstrated that changes in phytoplankton biomass determined by microscopy were correlated significantly (<em>p<</em>0.005) with variations in HPLC-derived concentrations of biomarker pigments (<em>r</em>² = 0.13–0.64) from all major algal groups, although HPLC tended to underestimate the relative abundance of cyanobacteria. Together, these findings show that while fertilisation of P-rich lakes with N can increase algal biomass, there is substantial variation in responses of genera and divisions to specific chemical forms of added N.</p> </div