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Summary: This paper is concerned with the formulation of N$$ N $$‐mixture models for estimating the abundance and probability of detection of a species from binary response, count and time‐to‐detection data. A modelling framework, which encompasses time‐to‐first‐detection within the context of detection/non‐detection and time‐to‐each‐detection and time‐to‐first‐detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed‐form expressions for the likelihoods associated with time‐to‐detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times‐to‐detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times‐to‐detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times‐to‐detection in addition to the count data. An R package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice. [ABSTRACT FROM AUTHOR]

Multinomial N‐mixture models are commonly used to fit data from a removal sampling protocol. If the mixing distribution is negative binomial, the distribution of the counts does not appear to have been identified, and practitioners approximate the requisite likelihood by placing an upper bound on the embedded infinite sum. In this paper, the distribution which underpins the multinomial N‐mixture model with a negative binomial mixing distribution is shown to belong to the broad class of multivariate negative binomial distributions. Specifically, the likelihood can be expressed in closed form as the product of conditional and marginal likelihoods and the information matrix shown to be block diagonal. As a consequence, the nature of the maximum likelihood estimates of the unknown parameters and their attendant standard errors can be examined and tests of the hypothesis of the Poisson against the negative binomial mixing distribution formulated. In addition, appropriate multinomial N‐mixture models for data sets which include zero site totals can also be constructed. Two illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this study, methods for efficient construction of A-, MV-, D- and E-optimal or near-optimal block designs for two-colour cDNA microarray experiments with array as the block effect are considered. Two algorithms, namely the array exchange and treatment exchange algorithms together with the complete enumeration technique are introduced. For large numbers of arrays or treatments or both, the complete enumeration method is highly computer intensive. The treatment exchange algorithm computes the optimal or near-optimal designs faster than the array exchange algorithm. The two methods however produce optimal or near-optimal designs with the same efficiency under the four optimality criteria. [ABSTRACT FROM AUTHOR]

The multiplicative binomial model was introduced as a generalization of the binomial distribution for modelling correlated binomial data. This distribution has not been extensively explored and is revisited in the present study. Some properties of the multiplicative binomial distribution, such as, expressions for the factorial moments and the information matrix, are investigated. The distribution is also extended to accommodate data arising from a Wadley's problem setting which is frequently encountered in dose–mortality studies and is one in which the number of organisms initially treated with a drug is unobserved. The Altham–Poisson distribution is introduced by modelling the unobserved initial number of organisms, as specified by n in the multiplicative binomial model, with a Poisson distribution and its suitability for overdispersed data from a Wadley's problem setting is explored. [ABSTRACT FROM AUTHOR]

Candidate locallyD-optimal designs for the binary two-variable logistic model with no interaction, which comprise 3 and 4 support points lying in the first quadrant of the two-dimensional Euclidean space, were introduced by Haines et al. (D-optimal designs for logistic regression in two variables. In: Lopez-Fidalgo J, Rodrigez-Diaz JM, Torsney B, editors. MODA8 – advances in model-oriented designs and analysis. Heidelberg: Physica-Verlag; 2007. p. 91–98). The authors proved algebraically the globalD-optimality of the 3-point design for the special case in which the intercept parameter is equal to−1.5434. However for other selected values of the intercept parameter, the globalD-optimality of the proposed 3- and 4-point designs was only demonstrated numerically. In this paper, we provide analytical proofs of theD-optimality of these 3- and 4-point designs for all negative and zero intercept parameters of the binary two-variable logistic model with no interaction. The results are extended to the construction ofD-optimal designs on a rectangular design space and illustrated by means of two examples of which one is a real example taken from the literature. [ABSTRACT FROM AUTHOR]

Response-adaptive randomization procedures are appropriate for clinical trials in which two or more treatments are to be compared, patients arrive sequentially and the response of each patient is recorded before the next patient arrives. However, for those procedures that involve sequential estimation of model parameters, start-up designs are commonly required in order to provide initial estimates of the parameters. In this paper, a suite of such start-up designs for two treatments and binary patient responses are considered and compared in terms of the numbers of patients required in order to give meaningful parameters estimates, the number of patients allocated to the better treatment, and the bias in the parameter estimates. It is shown that permuted block designs with blocks of size 4 are to be preferred over a wide range of parameter values. For the case of two treatments, normal responses and selected start-up procedures, a design incorporating complete randomization followed appropriately by repeats of one of the treatments yields the minimum expected number of patients and is to be preferred. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In dose-response studies, Wadley’s problem occurs when the number of organisms that survive exposure to varying doses of a treatment is observed but the number initially present is unknown. The unknown number of organisms initially treated has traditionally been modelled by a Poisson distribution, resulting in a Poisson distribution for the number of survivors with parameter proportional to the probability of survival. Data in this setting are often overdispersed. This study revisits the beta-Poisson distribution and considers its effectiveness in modelling overdispersed data from a Wadley’s problem setting. [ABSTRACT FROM PUBLISHER]

Testing for purchasing power parity (PPP) and uncovered interest parity (UIP) has been the focus of many empirically oriented studies. While these simple economic theories of exchange rate and interest rate determination are theoretically attractive, the empirical support for these equilibrium conditions is at best mixed. Many potential reasons have been cited in the literature for the failure of such studies, ranging from market imperfections to inappropriate modelling strategies. The current state-of-the-art procedure involves testing for two cointegrating vectors in a multivariate error correction model which may be economically identified as the PPP and UIP relations. However, such a procedure does not account for policy regime shifts which distort the underlying PPP and UIP relations. In this paper, a Markov-switching vector error correction model (VECM) is considered for time series data in which monetary and exchange rate regime shifts are known to be present. Weak evidence in favour of PPP and UIP is established in a standard linear VECM, although the residuals of this model indicate that it is inappropriate in terms of functional form. The Markov-switching VECM, however, provides convincing evidence in favour of both the PPP and UIP relations and a marked improvement in the residual distributions. [ABSTRACT FROM AUTHOR]