Parsimonious Solution Research Articles

Identification of Cancer-Related Symptom Clusters: An Empirical Comparison of Exploratory Factor Analysis Methods

ContextSymptom clusters, important for symptom management strategies, have been determined empirically by various analytical methods. Guidance to select methods from the options available in standard statistical packages is limited. ObjectivesTo compare alternative common factor analysis (FA) extraction methods appropriate to the data, to assess whether or not they determine similar symptom clusters, and to propose analytical approaches that are useful in this clinical context. MethodsWithin one month of commencing chemotherapy, outpatients from oncology and hematology clinics (n = 202) reported their symptom experience on a modified Rotterdam Symptom Checklist. Symptom distress levels in the past week were rated on a scale of one (not at all) to four (very much). In a secondary data analysis of 42 symptoms, the associations between symptoms and factors were determined using alternative common FA methods: principal axis factoring, unweighted least squares, image factor analysis, and alpha factor analysis (AFA). Symptom inclusion in a cluster was based on the interpretation of pattern and structure coefficients, and importantly, clinical relevance of the grouping. ResultsFive symptom clusters were commonly identified across methods: musculoskeletal discomforts/lethargy, oral discomforts, upper gastrointestinal discomforts, vasomotor symptoms, and gastrointestinal toxicities. In AFA, three additional clusters were lethargy, somatic symptoms, and treatment-related symptom clusters. ConclusionThe most parsimonious solution resulted from principal axis factoring, but for large numbers of symptoms, AFA may be superior by identifying symptom clusters more useful for symptom management. Interpreting complex symptom relationships may lead to the investigation of pathophysiological mechanisms and intervention opportunities. Future studies should include psychological and cognitive symptoms.

Model uncertainty in ancestral area reconstruction: A parsimonious solution?

AbstractIncreasingly complex likelihood–based methods are being developed to infer biogeographic history. The results of these methods are highly dependent on the underlying model which should be appropriate for the scenario under investigation. Our example concerns the dispersal among the southern continents of the grass subfamily Danthonioideae (Poaceae). We infer ancestral areas and dispersals using likelihood–based Bayesian methods and show the results to be indecisive (reversible–jump Markov chain Monte Carlo; RJ–MCMC) or contradictory (continuous–time Markov chain with Bayesian stochastic search variable selection; BSSVS) compared to those obtained under Fitch parsimony (FP), in which the number of dispersals is minimised. The RJ–MCMC and BSSVS results differed because of the differing (and not equally appropriate) treatments of model uncertainty under these methods. Such uncertainty may be unavoidable when attempting to infer a complex likelihood model with limited data, but we show with simulated data that it is not necessarily a meaningful reflection of the credibility of a result. At higher overall rates of dispersal FP does become increasingly inaccurate. However, at and below the rate observed in Danthonioideae multiple dispersals along branches are not observed and the correct root state can be inferred reliably. Under these conditions parsimony is a more appropriate model.

Transdimensional tomography with unknown data noise

SummaryA meaningful interpretation of seismic measurements requires a rigorous quantification of the uncertainty. In an inverse problem, the data noise determines how accurately observations should be fit, and ultimately the level of detail contained in the recovered model. A common problem in seismic tomography is the difficulty in quantifying data uncertainties, and thus the required level of data fit. Traditionally, the complexity of the solution model (defined by both the number of basis functions and the regularization) is defined arbitrarily by the user prior to inversion with only limited use of data errors. In the context of multiscale problems, dealing with multiple data sets that are characterized by different noise variances and that span the Earth at different scales is a major challenge. Practitioners are usually required to arbitrarily weigh the contribution of each data type into the final solution. Furthermore, the basis functions are usually spatially uniform across the velocity field and regularization procedures are global, which prevents the solution model from accounting for the uneven spatial distribution of information. In this work we propose to address these issues with a Hierarchical Bayesian inversion. The new algorithm represents an extension of the transdimensional tomography to account for uncertainties in data noise. This approach has the advantage of treating the level of noise in each data set, as well as the number of model parameters, as unknowns in the inversion. It provides a parsimonious solution that fully represents the degree of knowledge one has about seismic structure (i.e. constraints, resolution and trade-offs). Rather than being forced to make decisions on parametrization, level of data fit and weights between data types in advance, as is often the case in an optimization framework, these choices are relaxed and instead constrained by the data themselves. The new methodology is presented in a synthetic example where both the data density and the underlying structure contain multiple length scales. Three ambient noise data sets that span the Australian continent at different scales are then simultaneously inverted to infer a multiscale tomographic image of Rayleigh wave group velocity for the Australian continent. The procedure turns out to be particularly useful when dealing with multiple data types with different unknown levels of noise as the algorithm is able to naturally adjust the fit to the different data sets and provide a velocity map with a spatial resolution adapted to the spatially variable information present in the data.

A systems framework to telecommunication policy: the Philippine experience, 1989‐2009

PurposeThis paper aims to present a dialogue‐based systems framework using two cases in the liberalization of Philippine telecoms.Design/methodology/approachThrough a meta‐analysis of government data, academic research and policy studies about Philippine telecoms, the paper presents a holistic view of the role of political, business, and social sectors in policy making and implementation.FindingsThe paper shows how intra‐ and inter‐sector dialogues have resulted in the liberalization and growth of the industry. Conversely, it shows how paucities among such dialogues have had consequences in terms of unutilized capacity and in an oversight about the medium of choice in promoting universal access. Moreover, the paper shows how policy is a product of local traditions and global policy trends.Social implicationsThe paper reinforces calls for states to consider technological innovation and adoption in addressing universal service goals. The Philippines also serves as a case study for other developing states which pursue an agenda of liberalization and deregulation.Originality/valueThe study shows the utility of a proposed dialogue‐based systems framework as a parsimonious solution to the complexity of policy studies.

Transdimensional inversion of receiver functions and surface wave dispersion

We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.

Validating a Hospital Medicines Formulary Survey in the Western Pacific Region—A global hospital pharmacy initiative based on the Basel Statements

BackgroundIn 2008, the Basel Statements were developed to reflect the future of hospital pharmacy worldwide. Included were a key set of statements regarding the expanding role of hospital pharmacists' influence on prescribing from the management of medicines formularies to being an active member of the therapeutic decision-making process. ObjectivesThis study aimed to validate a survey to measure Basel Statement 26 regarding the role of medicines formularies and the factors that affect its use in the Western Pacific Region (WPR). MethodsThe survey was developed in consultation with a WPR advisory group and current literature. The survey was translated using the forward-backward method into Chinese (simplified) and Vietnamese. The instrument was pilot tested in a stratified random sample of 260 hospital pharmacy directors in the WPR. Principal components analysis (PCA) was applied to the data to assess construct validity of the Medicines Formulary Scale that assessed responders’ perceptions of their formulary and impact on utilization. ResultsThe Medicines Formulary Survey was completed by 107 hospital pharmacy directors or equivalent. The survey contained the Medicines Formulary Scale in addition to questions regarding the content and review process of the hospital’s formulary as well as demographic questions. Application of the PCA procedures resulted in a parsimonious 2-factor solution in which 33.8% of the variance was explained. The Cronbach alpha for the 17-item scale was found to be 0.70. The Cronbach alpha values for the first and second factor/subscales were 0.76 and 0.68, respectively. ConclusionThe Medicines Formulary Survey appears reliable and valid for assessing hospital pharmacy directors’ perceptions of hospital medicine formularies in the WPR. Further development of validated instruments to assess other areas of hospital pharmacy practice will help track the progression of hospital pharmacy and aid in globalization of the profession.

Reply to McNally and Tanner: Generosity evolves when cooperative decisions must be made under uncertainty

We thank McNally and Tanner (1) for their considered critique of our article (2). Our article addressed the puzzle of why humans, in one-shot interactions, often choose to incur costs to allocate benefits to others, with no possibility of recouping these losses (i.e., “irrational” generosity) (2). This empirical pattern challenges standard models of economic and evolutionary rationality, and has prompted the development of ever-more-cumbersome explanations (e.g., group selection, gene–culture coevolution, cultural group selection)—models fragilely dependent on many hard-to-verify assumptions. In our article, we demonstrated that the well-documented selective regime of direct reciprocity produces agents willing to cooperate in apparently one-shot encounters, when the cognitive problem of discriminating one-shot from repeated encounters under uncertainty has been incorporated into the analysis (as, realistically, it must be). This is a parsimonious solution to the puzzle that flows naturally out of well-understood selection pressures.

Clinicians' attitudes to depression in Europe: a pooled analysis of Depression Attitude Questionnaire findings

Depression in primary care is common but under-recognized and suboptimally managed. Health professionals' attitudes are likely to play an important part in their recognition and management of depression. To pool findings from studies using the Depression Attitude Questionnaire (DAQ) to provide greater detail of clinicians' attitudes and the measure's psychometric properties. Electronic databases and grey literature were searched for relevant studies. Data from eligible studies were requested and pooled analysis conducted. Twenty studies were eligible and data were obtained from 12 of these involving GPs (n = 1543) and nurses (n = 984). Responses showed strong disagreement that depression is due to ageing or weakness. European GPs were more positive about depression treatments than UK GPs; nurses were more favourable about psychotherapy than GPs. UK GPs especially strongly opposed notions that depression is best managed by psychiatrists. Trends over time indicated increasing acknowledgement of psychological therapies and the nurse's role in depression management. Factor analysis indicated that many DAQ items fitted weakly within an overall model. The most parsimonious solution involved two factors: a positive view of depression and its treatment response and professional confidence in depression management. Individual DAQ items appear to measure key aspects of clinicians' attitudes to depression, and item responses indicate important differences between professions and geographical settings as well as changes over time. There are problems with the DAQ as a scale: its internal consistency is weak, and several items appear specific to particular professions or service structures, indicating that this questionnaire should be revised.

Mechanisms of Sperm Storage in the Female Reproductive Tract: an Interspecies Comparison

Once semen has been collected for artificial insemination, it is diluted into extenders designed to prevent its deterioration over the period prior to insemination. If the semen is not frozen, the extenders provide protection for a period of a few hours to a few days, depending on species. Despite the efforts of biotechnologists to increase the duration of storage without compromising fertility, there has been relatively little progress for many years. However, comparative studies in diverse species have revealed that long-term sperm storage (up to months and years) within the female reproductive tract is relatively commonplace in reptiles, fishes, birds and amphibians. Even among mammals, some species of bat have evolved mechanisms for storing spermatozoa for several months in the uterus or oviduct so that they can mate in the autumn but postpone fertilization until the spring. We currently know little about the mechanisms that support such long-term sperm storage, mainly because evidence from such species is either absent or fragmentary. Nevertheless, parallels between mammalian and other systems, where spermatozoa are sequestered in sperm storage tubules, suggest that the enclosure of spermatozoa within pockets of epithelial cells may be sufficient to achieve long-term sperm storage. In addition, recent evidence from sperm-storing bats has suggested an alternative, or additional, hypothesis that the modulation of apoptosis within epithelial cells is important in controlling sperm survival. Despite a lack of direct experimental evidence from a wide variety of species, I propose that there is now enough evidence to warrant investigation of these hypotheses.

Exploring When Maternal Interest is Sufficient for High Attainment in Mathematics: A Configurational Analysis Using Longitudinal Data

Qualitative Comparative Analysis (QCA) is a case-based method, developed by Ragin (1987, 2000), to analyse mediumand large-n datasets. It uses Boolean algebra to show which configurations of factors in a model are either necessary and/or sufficient for a specified outcome. In the social world, we rarely see perfect necessity and sufficiency but we can use QCA to assess the degree of necessity or sufficiency to find configurations which are quasi-necessary or quasisufficient. In this paper, I use crisp-set QCA on data from the 1970 Birth Cohort Study (BCS70) to investigate which configurations of sex, maternal interest, social class and, later, ability are quasi-sufficient for various levels of attainment in maths. Firstly, I explain how to conduct QCA, through the use of examples, before using a set-theoretic measure of consistency to explore the relationship between sex, social class, maternal interest and, what I term, above-average attainment in mathematics. To this model, I then introduce an additional factor of general ability (operationalised as several dichotomous factors, each indicating a certain level of ability) leading to instances of configurations having strong subset relations but containing very few cases. These rows, called remainders, cannot be included in a solution without theoretical justification (Ragin, 2008). For the final stage of the analysis, I create, for two different general ability levels, a „most-complex solution‟ (which excludes all remainder rows) and a parsimonious solution (which includes any remainder row contributing to parsimony). These act as boundaries for the „intermediate solution‟ which contains only those remainders which can, theoretically, be thought to obtain the outcome. I then discuss each intermediate solution and note that, in one case, it is the same as the relevant most-complex version.

Proactive recruitment predicts participant retention to end of treatment in a secondhand smoke reduction trial with low-income maternal smokers

Improving smoking intervention trial retention in underserved populations remains a public health priority. Low retention rates undermine clinical advancements that could reduce health disparities. To examine the effects of recruitment strategies on participant retention among 279 low-income, maternal smokers who initiated treatment in a 16-week behavioral counseling trial to reduce child secondhand smoke exposure (SHSe). Participants were recruited using either reactive strategies or methods that included proactive strategies. Logistic regression analysis was used to test associations among retention and recruitment method in the context of other psychosocial and sociodemographic factors known to relate to retention. Backwards stepwise procedures determined the most parsimonious solution. Ninety-four percent of participants recruited with proactive + reactive methods were retained through end of treatment compared to 74.7% of reactive-recruited participants. Retention likelihood was five times greater if participants were recruited with proactive + reactive strategies rather than reactive recruitment alone (odds ration [OR] = 5.36; confidence interval [CI], 2.31-12.45). Greater knowledge of SHS consequences (OR = 1.58; CI, 1.07-2.34) was another significant factor retained in the final LR model. Proactive recruitment may improve retention among underserved smokers in behavioral intervention trials. Identifying factors influencing retention may improve the success of recruitment strategies in future trials, in turn, enhancing the impact of smoking interventions.

The geography of air freight: connections to U.S. metropolitan economies

Despite the rapid growth of air freight shipments, much of the existing literature on the geography of air transportation has paid more attention to passenger travel than air freight. The purpose of this paper is to elevate our understanding of air freight by determining which specific variables most influence and shape the geographic distribution of air freight by metropolitan area using stepwise regression analysis. The empirical results suggest a regression model of five independent variables was the most parsimonious solution where the final model accounted for 71.1% of the variation in air freight shipments by metropolitan area (MA). The most important predictor was the traffic shadow effect, where less populated MAs under the traffic shadow of larger MAs tended to generate lower levels of freight. The model also suggested that other key predictors included the employment market share in transportation-shipping-logistics industries, per capita personal income, the number of medical diagnostic and supplier establishments, and above average wages in high technology. Overall, metropolitan markets with diverse and efficient ground support systems, freight forwarders and other transportation services, a more affluent population, an intense agglomeration of medical laboratories and related suppliers, and a well paid skilled workforce engaged in computer systems design and electronic product manufacturing are more likely to ship freight by air.

Trans‐dimensional geoacoustic inversion.

This paper applies a general trans‐dimensional Bayesian methodology to geoacoustic inversion. Trans‐dimensional inverse problems are a generalization of fixed‐dimensional inversion that include the number and type of model parameters as unknowns in the problem. By extending the inversion state space to multiple sub‐spaces of different dimensionality, the posterior probability density quantifies the state of knowledge regarding inversion parameters, including effects due to limited knowledge about appropriate parametrization of the environment and error processes. The algorithm applies a reversible‐jump Markov chain and the seabed is parametrized as a partition model. The unknown data errors are addressed by including data‐error standard deviations as unknowns. Dimensional jumps are implemented with a birth‐death methodology that allows transitions between dimensions by adding or removing sediment interfaces to/from the partition model while maintaining unbiased sampling. Trans‐dimensional inversion results in an inherently parsimonious solution while partition modeling provides a naturally self‐regularizing algorithm based on data information content. Together, this results in environmental estimates that quantify appropriate seabed structure as supported by the data, allowing sharp discontinuities while approximating smooth transitions where needed. This approach applies generally to geoacoustic inversion and is illustrated here for seabed reflection coefficient data collected on the Malta Plateau. [Work supported by ONR.]

Neural Computations Governing Spatiotemporal Pooling of Visual Motion Signals in Humans

The brain estimates visual motion by decoding the responses of populations of neurons. Extracting unbiased motion estimates from early visual cortical neurons is challenging because each neuron contributes an ambiguous (local) representation of the visual environment and inherently variable neural response. To mitigate these sources of noise, the brain can pool across large populations of neurons, pool the response of each neuron over time, or a combination of the two. Recent psychophysical and physiological work points to a flexible motion pooling system that arrives at different computational solutions over time and for different stimuli. Here we ask whether a single, likelihood-based computation can accommodate the flexible nature of spatiotemporal motion pooling in humans. We examined the contribution of different computations to human observers' performance on two global visual motion discriminations tasks, one requiring the combination of motion directions over time and another requiring their combination in different relative proportions over space and time. Observers' perceived direction of global motion was accurately predicted by a vector average readout of direction signals accumulated over time and a maximum likelihood readout of direction signals combined over space, consistent with the notion of a flexible motion pooling system that uses different computations over space and time. Additional simulations of observers' performance with a population decoding model revealed a more parsimonious solution: flexible spatiotemporal pooling could be accommodated by a single computation that optimally pools motion signals across a population of neurons that accumulate local motion signals on their receptive fields at a fixed rate over time.

The human semicircular canal model of galvanic vestibular stimulation

A vector summation model of the action of galvanic stimuli on the semicircular canals has been shown to explain empirical balance and perceptual responses to binaural-bipolar stimuli. However, published data suggest binaural-monopolar stimuli evoke responses that are in the reverse direction of the model prediction. Here, we confirm this by measuring balance responses to binaural-monopolar stimulation as movements of the upper trunk. One explanation for the discrepancy is that the galvanic stimulus might evoke an oppositely directed balance response from the otolith organs that sums with and overrides the semicircular canal response. We tested this hypothesis by measuring sway responses across the full range of head pitch. The results showed some modulation of sway with pitch such that the maximal response occurred with the head in the primary position. However, the effect fell a long way short of that required to reverse the canal sway response. This indicates that the model is incomplete. Here, we examine alterations to the model that could explain both the bipolar and monopolar-evoked behavioural responses. An explanation was sought by remodelling the canal response with more recent data on the orientation of the individual canals. This improved matters but did not reverse the model prediction. However, the model response could be reversed by either rotating the entire labyrinth in the skull or by altering the gains of the individual canals. The most parsimonious solution was to use the more recent canal orientation data coupled with a small increase in posterior canal gain.

Statistical analysis and interpretation in a follow-up study of prelingually deaf children implanted before 5 years of age.

One important challenge in the follow-up study was the need to develop composite measures that were highly reliable and equally representative of communication skills measured at two distinct developmental periods. A second challenge was the need to partition variance in the outcome variables among conceptually important sets of variables in an attempt to identify unique and significant predictors and to identify likely pathways of influence. A final challenge was the need to preserve sample size in the presence of attrition from the initial data collection period and missing data. Primary analyses were based on principal components analysis to form composite measures of highly correlated variables followed by hierarchical multiple regression to determine the contribution of predictor sets ordered to reflect important causal assumptions and conceptual questions. The principal components analyses resulted in unidimensional, highly reliable composite measures of communication skill, educational environment, and information processing. The hierarchical multiple regression analyses allowed partitioning variance to isolate the unique contributions made by particular variables or sets of variables. Importantly, these analyses also allowed inferences about pathways of influence from early predictors to later outcomes. Multiple imputation was used to construct complete data sets, preserving power and consistency across the numerous analyses. Collectively, the chosen statistical analyses provide a pragmatic and parsimonious solution to the challenges posed by the data collected in this study. The analyses allowed clear conclusions about the major predictors of early and late communication skill in this sample and identified likely pathways through which early child, family, and educational environment variables have their influence.

The nomenclatural status of the nomina of amphibians and reptiles created by Garsault (1764), with a parsimonious solution to an old nomenclatural problem regarding the genus Bufo (Amphibia, Anura), comments on the taxonomy of this genus, and comments on some nomina created by Laurenti (1768)

The nomenclatural status of the nomina of amphibians and reptiles created by Garsault (1764), with a parsimonious solution to an old nomenclatural problem regarding the genus Bufo (Amphibia, Anura), comments on the taxonomy of this genus, and comments on some nomina created by Laurenti (1768)

Trans-dimensional geoacoustic inversion

This paper develops a general trans-dimensional Bayesian methodology for geoacoustic inversion. Trans-dimensional inverse problems are a generalization of fixed-dimensional inversion that includes the number and type of model parameters as unknowns in the problem. By extending the inversion state space to multiple subspaces of different dimensions, the posterior probability density quantifies the state of knowledge regarding inversion parameters, including effects due to limited knowledge about appropriate parametrization of the environment and error processes. The inversion is implemented here using a reversible-jump Markov chain Monte Carlo algorithm and the seabed is parametrized using a partition model. Unknown data errors are addressed by including a data-error model. Jumps between dimensions are implemented with a birth-death methodology that allows transitions between dimensions by adding or removing interfaces while maintaining detailed balance in the Markov chain. Trans-dimensional inversion results in an inherently parsimonious solution while partition modeling provides a naturally self-regularizing algorithm based on data information content, not on subjective regularization functions. Together, this results in environmental estimates that quantify appropriate seabed structure as supported by the data, allowing sharp discontinuities while approximating smooth transitions where needed. This approach applies generally to geoacoustic inversion and is illustrated here with seabed reflection-coefficient data.

Two-stage extreme learning machine for regression

Extreme learning machine (ELM) proposed by Huang et al. was developed for generalized single hidden layer feedforward networks (SLFNs) with a wide variety of hidden nodes. It proved to be very fast and effective especially for solving function approximation problems with a predetermined network structure. However, the method for determining the network structure of preliminary ELM may be tedious and may not lead to a parsimonious solution. In this paper, a systematic two-stage algorithm (named TS-ELM) is introduced to handle the problem. In the first stage, a forward recursive algorithm is applied to select the hidden nodes from the candidates randomly generated in each step and add them to the network until the stopping criterion achieves its minimum. The significance of each hidden node is then reviewed in the second stage and the insignificance ones are removed from the network, which drastically reduces the network complexity. The effectiveness of TS-ELM is verified by the empirical studies in this paper.

A model for correlation within clusters and its use in pollen analysis

Many methods of cluster analysis do not explicitly account for correlation between attributes. In this paper we explicitly model any correlation using a single factor within each cluster: i.e., the correlation of atributes within each cluster is adequately described by a single component axis. However, the use of a factor is not required in every cluster. Using a Minimum Message Length criterion, we can determine the number of clusters and also whether the model of any cluster is improved by introducing a factor. The technique allows us to seek clusters which reflect directional changes rather than imposing a zonation constrained by spatial (and implicitly temporal) position. Minimal message length is a means of utilising Okham’s Razor in inductive analysis. The ‘best’ model is that which allows most compression of the data, which results in a minimal message length for the description. Fit to the data is not a sufficient criterion for choosing models because more complicated models will almost always fit better. Minimum message length combines fit to the data with an encoding of the model and provides a Bayesian probability criterion as a means of choosing between models (and classes of model). Applying the analysis to a pollen diagram from Southern Chile, we find that the introduction of factors does not improve the overall quality of the mixture model. The solution without axes in any cluster provides the most parsimonious solution. Examining the cluster with the best case for a factor to be incorporated in its description shows that the attributes highly loaded on the axis represent a contrast of herbaceous vegetation and dominant forests types. This contrast is also found when fitting the entire population, and in this case the factor solution is the preferred model. Overall, the cluster solution without factors is much preferred. Thus, in this case classification is preferred to ordination although more data are desirable to confirm such a conclusion.