Ratios of Parameters: Some Econometric Examples

Lye, Jenny; Hirschberg, Joe

doi:10.1111/1467-8462.12300

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…The resulting ratio coefficient was 0.76, and although this was higher than the known land uplift, the approximate confidence interval included the known land uplift. For comparison, we here calculate the same ratio, and also provide an approximate 95% confidence interval calculated using Fieller's theorem (see Lye & Hirschberg, 2018, equation 10).…”

Section: Worked Examplesmentioning

confidence: 99%

Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling

2022

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In community ecology, unconstrained ordination can be used to indirectly explore drivers of community composition, while constrained ordination can be used to directly relate predictors to an ecological community. However, existing constrained ordination methods do not explicitly account for community composition that cannot be explained by the predictors, so that they have the potential to misrepresent community composition if not all predictors are available in the data. We propose and develop a set of new methods for ordination and joint species distribution modelling (JSDM) as part of the generalized linear latent variable model (GLLVM) framework, that incorporate predictors directly into an ordination. This includes a new ordination method that we refer to as concurrent ordination, as it simultaneously constructs unconstrained and constrained latent variables. Both unmeasured residual covariation and predictors are incorporated into the ordination by simultaneously imposing reduced rank structures on the residual covariance matrix and on fixed‐effects. We evaluate the method with a simulation study, and show that the proposed developments outperform canonical correspondence analysis (CCA) for Poisson and Bernoulli responses, and perform similar to redundancy analysis (RDA) for normally distributed responses, the two most popular methods for constrained ordination in community ecology. Two examples with real data further demonstrate the benefits of concurrent ordination, and the need to account for residual covariation in the analysis of multivariate data. This article contextualizes the role of constrained ordination in the GLLVM and JSDM frameworks, while developing a new ordination method that incorporates the best of unconstrained and constrained ordination, and which overcomes some of the deficiencies of existing classical ordination methods.

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Section: Worked Examplesmentioning

confidence: 99%

Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling

2022

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“…The resulting ratio coefficient was 0.76, and although this was higher than the known land uplift, the approximate confidence interval included the known land uplift. For comparison, we here calculate the same ratio, and also provide an approximate 95% confidence interval calculated using Fieller’s theorem (see Lye & Hirschberg 2018, equation 10).…”

Section: Worked Examplesmentioning

confidence: 99%

Concurrent ordination: simultaneous unconstrained and constrained latent variable modeling

Veen¹,

Hui²,

O’Hara³

2021

Preprint

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In community ecology, unconstrained ordination can be used to predict latent variables from a multivariate dataset, which generated the observed species composition. Latent variables can be understood as ecological gradients, which are represented as a function of measured predictors in constrained ordination, so that ecologists can better relate species composition to the environment while reducing dimensionality of the predictors and the response data. However, existing constrained ordination methods do not explicitly account for information provided by species responses, so that they have the potential to misrepresent community structure if not all predictors are measured. We propose a new method for model-based ordination with constrained latent variables in the Generalized Linear Latent Variable Model framework, which incorporates both measured predictors and residual covariation to optimally represent ecological gradients. Simulations of unconstrained and constrained ordination show that the proposed method outperforms CCA and RDA.

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The mean, variance, and bias of the OLS based estimator of the extremum of a quadratic regression model for small samples

Rosenblad

2020

Communications in Statistics - Theory and Methods

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Ratios of Parameters: Some Econometric Examples

Cited by 3 publications

References 29 publications

Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling

Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling

Concurrent ordination: simultaneous unconstrained and constrained latent variable modeling

The mean, variance, and bias of the OLS based estimator of the extremum of a quadratic regression model for small samples

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