Canonical correspondence analysis in social science research

The use of simple and multiple correspondence analysis is well-established in socialscience research for understanding relationships between two or more categorical variables.By contrast, canonical correspondence analysis, which is a correspondence analysis with linearrestrictions on the solution, has become one of the most popular multivariate techniques inecological research. Multivariate ecological data typically consist of frequencies of observedspecies across a set of sampling locations, as well as a set of observed environmental variablesat the same locations. In this context the principal dimensions of the biological variables aresought in a space that is constrained to be related to the environmental variables. Thisrestricted form of correspondence analysis has many uses in social science research as well,as is demonstrated in this paper. We first illustrate the result that canonical correspondenceanalysis of an indicator matrix, restricted to be related an external categorical variable, reducesto a simple correspondence analysis of a set of concatenated (or stacked ) tables. Then weshow how canonical correspondence analysis can be used to focus on, or partial out, aparticular set of response categories in sample survey data. For example, the method can beused to partial out the influence of missing responses, which usually dominate the results of amultiple correspondence analysis.

Generalized canonical correlation analysis of matrices with different row and column orders

A Method is offered that makes it possible to apply generalized canonicalcorrelations analysis (CANCOR) to two or more matrices of different row and column order. The new method optimizes the generalized canonical correlationanalysis objective by considering only the observed values. This is achieved byemploying selection matrices. We present and discuss fit measures to assessthe quality of the solutions. In a simulation study we assess the performance of our new method and compare it to an existing procedure called GENCOM,proposed by Green and Carroll. We find that our new method outperforms the GENCOM algorithm both with respect to model fit and recovery of the truestructure. Moreover, as our new method does not require any type of iteration itis easier to implement and requires less computation. We illustrate the methodby means of an example concerning the relative positions of the political parties inthe Netherlands based on provincial data.

The contributions of rare objects in correspondence analysis

Correspondence analysis, when used to visualize relationships in a table of counts(for example, abundance data in ecology), has been frequently criticized as being too sensitiveto objects (for example, species) that occur with very low frequency or in very few samples. Inthis statistical report we show that this criticism is generally unfounded. We demonstrate this inseveral data sets by calculating the actual contributions of rare objects to the results ofcorrespondence analysis and canonical correspondence analysis, both to the determination ofthe principal axes and to the chi-square distance. It is a fact that rare objects are oftenpositioned as outliers in correspondence analysis maps, which gives the impression that theyare highly influential, but their low weight offsets their distant positions and reduces their effecton the results. An alternative scaling of the correspondence analysis solution, the contributionbiplot, is proposed as a way of mapping the results in order to avoid the problem of outlying andlow contributing rare objects.

Fuzzy coding in constrained ordinations

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example, environmental variables, spatial positions of samples). In this report I demonstrate the advantages of the fuzzy coding of explanatory variables: first, nonlinear relationships can be diagnosed; second, more variance in the responses can be explained; and third, in the presence of categorical explanatory variables (for example, years, regions) the interpretation of the resulting triplot ordination is unified because all explanatory variables are measured at a categorical level.

Discriminating crop, weeds and soil surface with a terrestrial LIDAR sensor

In this study, the evaluation of the accuracy and performance of a light detection and ranging (LIDAR) sensor for vegetation using distance and reflection measurements aiming to detect and discriminate maize plants and weeds from soil surface was done. The study continues a previous work carried out in a maize field in Spain with a LIDAR sensor using exclusively one index, the height profile. The current system uses a combination of the two mentioned indexes. The experiment was carried out in a maize field at growth stage 12–14, at 16 different locations selected to represent the widest possible density of three weeds: Echinochloa crus-galli (L.) P.Beauv., Lamium purpureum L., Galium aparine L.and Veronica persica Poir.. A terrestrial LIDAR sensor was mounted on a tripod pointing to the inter-row area, with its horizontal axis and the field of view pointing vertically downwards to the ground, scanning a vertical plane with the potential presence of vegetation. Immediately after the LIDAR data acquisition (distances and reflection measurements), actual heights of plants were estimated using an appropriate methodology. For that purpose, digital images were taken of each sampled area. Data showed a high correlation between LIDAR measured height and actual plant heights (R2 = 0.75). Binary logistic regression between weed presence/absence and the sensor readings (LIDAR height and reflection values) was used to validate the accuracy of the sensor. This permitted the discrimination of vegetation from the ground with an accuracy of up to 95%. In addition, a Canonical Discrimination Analysis (CDA) was able to discriminate mostly between soil and vegetation and, to a far lesser extent, between crop and weeds. The studied methodology arises as a good system for weed detection, which in combination with other principles, such as vision-based technologies, could improve the efficiency and accuracy of herbicide spraying.

Land use changes, landscape ecology and their socioeconomic driving forces in the Spanish Mediterranean coast (the Maresme County, 1850-2005)

[cat] Utilitzem un conjunt de mètriques del paisatge per estudiar l'evolució a llarg termini seguida en una típica zona costanera del Mediterrani des de 1850 fins a 2005, que mostren una greu deterioració del medi ambient entre 1950 i 2005. Les principals forces motores d'aquesta degradació del paisatge han estat el creixement urbà experimentat a les antigues zones agrícoles situades a les planes litorals, juntament amb l'abandonament i la reforestació dels vessants dels pujols interceptats per àrees residencials de baixa densitat, carreteres i altres infraestructures lineals. Duem a terme una anàlisi estadística de redundància (RDA) amb la finalitat d'identificar els que considerem com alguns agents rectors socioeconòmics i polítics d'última instància d'aquests impactes ambientals. Els resultats confirmen les nostres hipòtesis interpretatives, que són que: 1) els canvis en les cobertes i usos del sòl determinen canvis en les propietats dels paisatge, tant estructurals com funcionals; 2) aquests canvis no es produeixen per atzar, sinó que estan relacionats amb factors geogràfics i forces socioeconòmiques i polítiques.

Land use changes, landscape ecology and their socioeconomic driving forces in the Spanish Mediterranean coast (the Maresme County, 1850-2005)

[cat] Utilitzem un conjunt de mètriques del paisatge per estudiar l'evolució a llarg termini seguida en una típica zona costanera del Mediterrani des de 1850 fins a 2005, que mostren una greu deterioració del medi ambient entre 1950 i 2005. Les principals forces motores d'aquesta degradació del paisatge han estat el creixement urbà experimentat a les antigues zones agrícoles situades a les planes litorals, juntament amb l'abandonament i la reforestació dels vessants dels pujols interceptats per àrees residencials de baixa densitat, carreteres i altres infraestructures lineals. Duem a terme una anàlisi estadística de redundància (RDA) amb la finalitat d'identificar els que considerem com alguns agents rectors socioeconòmics i polítics d'última instància d'aquests impactes ambientals. Els resultats confirmen les nostres hipòtesis interpretatives, que són que: 1) els canvis en les cobertes i usos del sòl determinen canvis en les propietats dels paisatge, tant estructurals com funcionals; 2) aquests canvis no es produeixen per atzar, sinó que estan relacionats amb factors geogràfics i forces socioeconòmiques i polítiques.

Environmental factors, spatial variation, and specific requirements of Chironomidae in Mediterranean reference streams

Chironomidae spatial distribution was investigated at 63 near-pristine sites in 22 catchments of the Iberian Mediterranean coast. We used partial redundancy analysis to study Chironomidae community responses to a number of environmental factors acting at several spatial scales. The percentage of variation explained by local factors (23.3%) was higher than that explained by geographical (8.5%) or regional factors(8%). Catchment area, longitude, pH, % siliceous rocks in the catchment, and altitude were the best predictors of Chironomidae assemblages. We used a k-means cluster analysis to classified sites into 3 major groups based on Chironomidae assemblages. These groups were explained mainly by longitudinal zonation and geographical position, and were defined as 1) siliceous headwater streams, 2) mid-altitude streams with small catchment areas, and 3) medium-sized calcareous streams. Distinct species assemblages with associated indicator taxa were established for each stream category using IndVal analysis. Species responses to previously identified key environmental variables were determined, and optima and tolerances were established by weighted average regression. Distinct ecological requirements were observed among genera and among species of the same genus. Some genera were restricted to headwater systems (e.g., Diamesa), whereas others (e.g., Eukiefferiella) had wider ecological preferences but with distinct distributions among congenerics. In the present period of climate change, optima and tolerances of species might be a useful tool to predict responses of different species to changes in significant environmental variables, such as temperature and hydrology.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Dynamic diagnosis based on interval analytical redundancy relations and signs of the symptoms

A model-based approach for fault diagnosis is proposed, where the fault detection is based on checking the consistencyof the Analytical Redundancy Relations (ARRs) using an interval tool. The tool takes into account the uncertainty in theparameters and the measurements using intervals. Faults are explicitly included in the model, which allows for the exploitation of additional information. This information is obtained from partial derivatives computed from the ARRs. The signs in the residuals are used to prune the candidate space when performing the fault diagnosis task. The method is illustrated using a two-tank example, in which these aspects are shown to have an impact on the diagnosis and fault discrimination, since the proposed method goes beyond the structural methods

Determinants of linear judgment: A meta-analysis of lens model studies

The mathematical representation of Brunswik s lens model has been usedextensively to study human judgment and provides a unique opportunity to conduct ameta-analysis of studies that covers roughly five decades. Specifically, we analyzestatistics of the lens model equation (Tucker, 1964) associated with 259 different taskenvironments obtained from 78 papers. In short, we find on average fairly high levelsof judgmental achievement and note that people can achieve similar levels of cognitiveperformance in both noisy and predictable environments. Although overall performancevaries little between laboratory and field studies, both differ in terms of components ofperformance and types of environments (numbers of cues and redundancy). An analysisof learning studies reveals that the most effective form of feedback is information aboutthe task. We also analyze empirically when bootstrapping is more likely to occur. Weconclude by indicating shortcomings of the kinds of studies conducted to date, limitationsin the lens model methodology, and possibilities for future research.

Tying up the loose ends in simple correspondence analysis

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

Correspondence analysis and categorical conjoint measurement

We show the equivalence between the use of correspondence analysis (CA)of concadenated tables and the application of a particular version ofconjoint analysis called categorical conjoint measurement (CCM). Theconnection is established using canonical correlation (CC). The second part introduces the interaction e¤ects in all three variants of theanalysis and shows how to pass between the results of each analysis.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

A semi-grand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: proton binding of carboxylated latex particles as a case study

In this paper, we present a computer simulation study of the ion binding process at an ionizable surface using a semi-grand canonical Monte Carlo method that models the surface as a discrete distribution of charged and neutral functional groups in equilibrium with explicit ions modelled in the context of the primitive model. The parameters of the simulation model were tuned and checked by comparison with experimental titrations of carboxylated latex particles in the presence of different ionic strengths of monovalent ions. The titration of these particles was analysed by calculating the degree of dissociation of the latex functional groups vs. pH curves at different background salt concentrations. As the charge of the titrated surface changes during the simulation, a procedure to keep the electroneutrality of the system is required. Here, two approaches are used with the choice depending on the ion selected to maintain electroneutrality: counterion or coion procedures. We compare and discuss the difference between the procedures. The simulations also provided a microscopic description of the electrostatic double layer (EDL) structure as a function of p H and ionic strength. The results allow us to quantify the effect of the size of the background salt ions and of the surface functional groups on the degree of dissociation. The non-homogeneous structure of the EDL was revealed by plotting the counterion density profiles around charged and neutral surface functional groups.