In optimal stopping problems, decision makers are assumed to search randomly to learn the utility of alternatives; in contrast, in one-shot multi-attribute utility optimization, decision makers are assumed to have perfect knowledge of utilities. We point out that these two contexts represent the boundaries of a continuum, of which the middle remains uncharted: How should people search intelligently when they possess imperfect information about the alternatives? We assume that decision makers first estimate the utility of each available alternative and then search the alternatives in order of their estimated utility until expected benefits are outweighed by search costs. We considered three well-known models for estimating utility: (i) a linear multi-attribute model, (ii) equal weighting of attributes, and (iii) a single-attribute heuristic. We used 12 real-world decision problems, ranging from consumer choice to industrial experimentation, to measure the performance of the three models. The full model (i) performed best on average but its simplifications (ii and iii) also had regions of superior performance. We explain the results by analyzing the impact of the models’ utility order and estimation error.

Although neurocognition is commonly described in terms of different functional domains, some factor analytic studies have suggested a simpler dimensional structure for neuropsychological (NP) tests in patients with schizophrenia. Standardized tasks of everyday functioning, or tests of “functional capacity” (FC), are viewed differently from traditional NP tests, and are hence used as a co-primary measure in treatment studies. However, FC and NP tests have been found to be highly correlated. In fact, a recent study of ours suggested that performances on these different types of tasks constituted a single latent trait in a cross-sectional analysis. The current study examined the longitudinal factor structure of a combined set of NP and FC tests. Patients with schizophrenia (n = 195) were examined at two assessment occasions separated by periods ranging from 6 weeks to 6 months. Participants were assessed with the MATRICS Consensus Cognitive Battery (MCCB) and two performance-based assessments of FC. A single latent trait was extracted using full information maximum likelihood procedures, and its temporal stability was examined in terms of: stability of the latent trait scores, the inter-correlations of the three indicators of the latent trait, and the stability of loadings for the FC and NP items underlying the latent trait at the two measurement occasions. All indices of temporal stability were confirmed, with stability not related to follow-up duration. Variation in clinical symptoms and treatments across the measurement occasions was negligible. These findings raise the question of whether cognitive abilities measured by NP tests and FC instruments are tapping a single ability construct, which might have shared causal influences as well. (JINS, 2013, 19, 1–8)

State politics researchers commonly employ ordinary least squares (OLS) regression or one of its variants to test linear hypotheses. However, OLS is easily influenced by outliers and thus can produce misleading results when the error term distribution has heavy tails. Here we demonstrate that median regression (MR), an alternative to OLS that conditions the median of the dependent variable (rather than the mean) on the independent variables, can be a solution to this problem. Then we propose and validate a hypothesis test that applied researchers can use to select between OLS and MR in a given sample of data. Finally, we present two examples from state politics research in which (1) the test selects MR over OLS and (2) differences in results between the two methods could lead to different substantive inferences. We conclude that MR and the test we propose can improve linear models in state politics research.

That ‘all foods can fit’ into a healthy diet is a long-standing principle of dietetic practice. The present study quantified the relative contributions of foods to encourage and foods to limit, using new techniques of individual diet optimisation and nutrient profiling. Individual foods from every food group were assigned to four nutrient profile classes based on the French SAIN,LIM system. Foods with the most favourable nutrient profiles were in class 1, and foods with the least favourable nutrient profiles were in class 4. An optimised diet that met the recommendations for thirty-two nutrients and that respected the existing eating habits was designed for each adult in the nationally representative ‘Enquête Individuelle et Nationale sur les Consommations Alimentaires 1’ dietary survey (n 1171). The relative proportions of the four nutrient profiling classes were assessed before and after the optimisation process. The contribution of fruits and vegetables, whole grains, milk and fish was significantly increased, whereas the contribution of refined grains, meats, mixed dishes, sugars and fats was decreased. The optimised diets derived more energy (30 v. 21 % in the observed diets) from class 1 foods and less energy (41 v. 56 %) from class 4 foods. They also derived a higher amount of class 1 foods (61 v. 51 %) and a lower amount of class 4 foods (22 v. 32 %). Thus, nutrient adequacy was compatible with the consumption of foods with an unfavourable nutrient profile (one-fifth the basket weight), provided that the diet also contained almost two-thirds of foods with the most favourable profile. Translating these results into concrete and quantified advice may have very tangible public health implications.

Introduction. Leaf area is often related to plant growth, development, physiology and yield. Many non-destructive models have been proposed for leaf area estimation of several plant genotypes, demonstrating that leaf length, leaf width and leaf area are closely correlated. Thus, the objective of our study was to develop a reliable model for leaf area estimation from linear measurements of leaf dimensions for citrus genotypes. Materials and methods. Leaves of citrus genotypes were harvested, and their dimensions (length, width and area) were measured. Values of leaf area were regressed against length, width, the square of length, the square of width and the product (length × width). The most accurate equations, either linear or second-order polynomial, were regressed again with a new data set; then the most reliable equation was defined. Results and discussion. The first analysis showed that the variables length, width and the square of length gave better results in second-order polynomial equations, while the linear equations were more suitable and accurate when the width and the product (length × width) were used. When these equations were regressed with the new data set, the coefficient of determination (R2) and the agreement index ‘d’ were higher for the one that used the variable product (length × width), while the Mean Absolute Percentage Error was lower. Conclusion. The product of the simple leaf dimensions (length × width) can provide a reliable and simple non-destructive model for leaf area estimation across citrus genotypes.

Let ${{\mathbb{F}}_{q}}$ be a finite field of $q$ elements, $\mathcal{F}$ a $p$-adic field, and $D$ a quaternion division algebra over $\mathcal{F}$. This paper proves uniqueness of Shalika models for $\text{G}{{\text{L}}_{2n}}\left( {{\mathbb{F}}_{q}} \right)$ and $\text{G}{{\text{L}}_{2n}}\left( D \right)$, and re-obtains uniqueness of Shalika models for $\text{G}{{\text{L}}_{2n}}\left( \mathcal{F} \right)$ for any $n\,\in \,\mathbb{N}$.

Restricted breeding seasons used in beef cattle produce censored data for reproduction traits measured in regard to these seasons. To analyze these data, adequate methods must be used. The objective of this paper was to compare three approaches aiming to evaluate sexual precocity in Nellore cattle. The final data set contained 6699 records of age at first conception (AFC14) (in days) and of heifer pregnancy (HP14) (binary) obtained from females exposed to the bulls for the first time at about 14 months of age. Records of females that did not calve in the following year after being exposed to a sire were considered censored (77.5% of total). The models used to obtain genetic parameters and expected progeny differences (EPDs) were a Weibull mixed and a censored linear model for AFC14 and threshold model for HP14. The mean heritabilities obtained were 0.76 and 0.44, respectively, for survival and censored linear models (for AFC14), and 0.58 for HP14. Ranking and Pearson correlations varied (in absolute values) from 0.54 to 0.99 (considering different percentages of sires selected), indicating moderate changes in the classification. Considering survival analysis as the best selection criterion (that would result in the best response to selection), it was observed that selection for HP14 would lead to a more significant decrease in selection response if compared with selection for AFC14 analysed by censored linear model, from which results were very similar to the survival analysis.

N-alkanes are long-chain saturated hydrocarbons occurring in plant cuticles that can be used as chemical markers for estimating the diet composition of herbivores. An important constraint of using n-alkanes to estimate diet composition with currently employed mathematical procedures is that the number of markers must be equal or larger than the number of diet components. This is a considerable limitation when dealing with free-ranging herbivores feeding on complex plant communities. We present a novel approach for the estimation of diet composition using n-alkanes which applies equally to cases where the number of markers is lower, equal or greater than the number of plant species in the diet. The model uses linear programming to estimate the minimum and maximum proportions of each plant in the diet, and avoids the need for grouping species in order to reduce the number of estimated dietary components. We illustrate the model with two data sets of n-alkane content of plants and faeces obtained from a sheep grazing experiment conducted in Australia and a red deer study in Portugal. Our results are consistent with previous studies on those data sets and provide additional information on the proportions of individual species in the diet. Results show that sheep included in the diet high proportions of white clover (from 0.25 to 0.37), and relatively high proportions of grasses (e.g. brome from 0.14 to 0.26) but tended to avoid Lotus spp. (always less than 0.04 of the diet). For red deer we found high proportions of legumes (e.g. Trifolium angustifolium and Vicia sativa reaching maximum proportions of 0.42 and 0.30 of the diet, respectively) with grasses being less important and Cistus ladanifer, a browse, also having relevance (from 0.21 to 0.42 of the diet).

Days open data from 113 569 lactation records in 774 Spanish Holstein herds were analysed using standard linear models under two different editing procedures, and with two alternative methodologies that account for censoring: a censored linear model (CLM) and a Weibull survival analysis (SA) model. The first editing procedure excluded from the linear model all censored records for days open (LMnc), and the second defined days open as days from calving to the last known insemination or culling date, treating censored records as complete (LM). Sire variance estimates for days open were 61, 70 and 139 for LMnc, LM and CLM, respectively, and 0·026 for SA on a logarithmic scale. Heritability estimates were 0·05, 0·06 and 0·08 with LMnc, LM and CLM, respectively. Rankings of sires varied between methodologies: sire evaluations from LMnc and LM had rank correlations with evaluations from SA equal to −0·65 and −0·82, respectively, and of 0·71 and 0·87 with evaluations from CLM. The rank correlation between evaluations from SA and CLM was −0·98, suggesting stronger agreement of sire rankings between models that take censoring into account.The SA model had a better predictive ability of daughter fertility at early stages of lactation than the other methods, as measured by chi-squared statistics for predicted pregnancy status at 75, 103, 140, or 200 days post partum in a split data set. The CLM also predicted daughter fertility more accurately than any of the two standard linear models.

The effect of tillage, clipping, precipitation and temperature on above-ground grass production was investigated in permanent plots at a Zambian savanna site for 5 y (1996^2001) by the harvest method. Mean species richness was 4.6 species m-2 with a total of 15 species at the study site. Mean end-of-season grass phytomass was 464 g m-2 with no statistically significant differences among years in control quadrats. Grass phytomass recovered within two wet seasons after tillage and a similar trend was observed after cessation of a 2-y monthly harvesting regime. However, in experimental quadrats, plot, treatment and year had significant effects on grass production. Previous- and current-season precipitation had no significant effect on end-of-wet-season grass phytomass but phytomass of the previous season explained 27-53% of the variation in end-of-wet-season phytomass. Grass production peaked in the wet season and declined sharply as the dry season progressed. The interaction between precipitation, temperature, harvesting and duration of the dry season explained 81-91% of the variation in daily grass production but the significance of the interactions varied with season and duration of harvesting. Precipitation-use efficiency (PUE) of grasses declined from 2.25 g m-2 mm-1 at the start of the wet season in December to 0.25 g m-2 mm-1 at the end of the season in March. Monthly harvesting for 1 y reduced PUE to less than 25%. The results indicate very complex relationships between above-ground grass production (dependent variable) and climate and land-use (independent) factors that makes the prediction of grass production in central southern African savannas difficult.

Data on lamb survival from birth to weaning of Rambouillet and Finnsheep were analysed with sire-maternal grandsire linear (LM) and threshold (TM) models. Models for the Rambouillet included the effects of year, type of birth, age of dam and sex as fixed effects and sire, maternal grandsire and residual as random effects. For the Finnsheep, fixed effects were year-age of dam combination, type of birth-rearing and sex, and random effects were sire, maternal grandsire and residual. Restricted maximum likelihood (REML) and marginal maximum likelihood (MML) estimates of variance and covariance components were obtained under LM and TM, respectively. The performance of LM and TM was assessed in terms of goodness of fit and predictive ability. Within the Rambouillet breed, heritabilities of additive direct (0·06), additive maternal (0·04) and total effects (0·13) obtained with TM were 2, 1·3 and 1·9 times greater than those obtained with LM, respectively. For the Finnsheep data, estimated heritabilities of direct (0·17), maternal (0·26) and total (0·34) effects using TM were 1·9, 1·4 and 1·6 times greater than the estimates using LM, respectively. Estimated genetic correlation between direct and maternal effects was 0·14 for the Finnsheep with both the LM and TM. Higher genetic correlations between direct and maternal effects (0·44 and 0·62 with LM and TM, respectively) were obtained for the Rambouillet data. Goodness of fit and predictive ability of the models used with the Finnsheep data were better than for the models used with the Rambouillet data, but within breed, no sizable or significant differences were detected between LM and TM. Results indicate that maternal effects were important in lamb survival to weaning; especially in the more prolific Finnsheep breed.

This paper considers the application of state space modelling to the chain ladder linear model in order to allow the run-off parameters to vary with accident year. In the usual application of the chain ladder technique, the development factors are assumed to be the same for each accident year. This implies that the run-off shape does not alter with accident year. This paper shows how this assumption can be relaxed in order to allow a recursive smooth model to be applied, or for large changes in the shape of the run-off curve. It is possible for these changes to be modelled using external inputs, or for a multiprocess model to be used to detect changes in the run-off shape.

This paper considers the application of loglinear models to claims run-off triangles which contain negative incremental claims. Maximum likelihood estimation is applied using the three parameter lognormal distribution. The method can be used in conjunction with any model which can be expressed in lognormal form. In particular the chain ladder technique is considered. An example is given and the results compared with the basic actuarial method.

This paper extends the theory of graduation by parametric formulae to include dynamic estimation methods. This is an application of the Kalman filter and allows the parameters of the curve fitted to vary with age. The amount of variation is determined by the amount of smoothing required, and the method can be regarded as a combination of curve fitting and sequential smoothing, each of which has been used separately for performing graduations. In practice, a dynamic straight line can always be used for the graduation and the method has a sensible logical interpretation.