Flexible generalized t-link models for binary response data

A critical issue in modelling binary response data is the choiceof the links. We introduce a new link based on the generalizedt-distribution. There are two parameters in the generalizedt-link: one parameter purely controls the heaviness of the tailsof the link and the second parameter controls the scale of thelink. Two major advantages are offered by the generalized t-links.First, a symmetric generalized t-link with an unknown shapeparameter is much more identifiable than a Student t-link withunknown degrees of freedom and a known scale parameter. Secondly,skewed generalized t-links with both unknown shape and scaleparameters provide much more flexible and improved skewed linkregression models than the existing skewed links. Various theoreticalproperties and attractive features of the proposed links areexamined and explored in detail. An efficient Markov chain MonteCarlo algorithm is developed for sampling from the posteriordistribution. The deviance information criterion measure isused for guiding the choice of links. The proposed methodologyis motivated and illustrated by prostate cancer data.     

Rank Tests for Complete Block Designs

In this article a general univariate K-sample rank test for complete block designs with proportional cell frequencies is derived. It is shown that the test statistic has under H₀ and for arbitrary scores asymptotically a X²-distribution with K — 1 degrees of freedom. Special cases of this test are the Kruskal-Wallis test and the Friedman test. The test is compared with the Benard-van-Elteren test, the Mack-Skillings test and a test proposed by Downton. Finally the application of the test is illustrated by two examples.     

Tables of Bonferroni-limits for Simultaneous F-Tests

Bonferroni adjusted F-tables are given for α=0.10 and α = 0.001 with degrees of freedom following classical tables of Fisher and Yates. The tables may be used in simultaneous analysis of variances or in evaluating binomial tests by means of F-tables in configural frequency testing.     

Confidence Limits on Heritability Under Non-normal Variations

Moment approximation for the non-normal sampling distribution of the ratio of mean squares in the balanced one-way Model II is found close to that of the Snedecor's F-distribution. The confidence limits for heritability of paternal half-sib correlations, derived employing F-distribution, are, in general, remarkably narrow for platykurtic and wide for leptokurtic sire effects than the normal limits. The effect of kurtosis of environmental deviations on these limits is of no consequence whereas the effect of skewness is invisible.     

Force treadmill for measuring vertical and horizontal ground reaction forces

Weconstructed a force treadmill to measure the vertical, horizontal andlateral components of the ground-reaction forces (F_z,F_y,F_x, respectively) and the ground-reaction force moments(M_z,M_y,M_x), respectively exerted bywalking and running humans. The chassis of a custom-built, lightweight(90 kg), mechanically stiff treadmill was supported along its length bya large commercial force platform. The natural frequencies of vibrationwere >178 Hz for F_z and >87Hz for F_y, i.e., well above thesignal content of these ground-reaction forces. Mechanical tests andcomparisons with data obtained from a force platform runway indicatedthat the force treadmill recordedF_z,F_y,M_x andM_y ground-reaction forces andmoments accurately. Although the lowest natural frequency of vibrationwas 88 Hz for F_x, thesignal-to-noise ratios for F_x andM_z were unacceptable. This devicegreatly decreases the time and laboratory space required for locomotionexperiments and clinical evaluations. The modular design allows forindependent use of both treadmill and force platform.

     

The S-Distribution A Tool for Approximation and Classification of Univariate,Unimodal Probability Distributions

In many statistical applications a data set needs to be evaluated but there is no solid information about which probability distribution might be most appropriate. Typical solutions to this problems are: to make assumptions that facilitate mathematical treatment; to use a family of distribution functions that contains all relevant distributions as special cases; or, to employ nonparametric methods. All three solutions have disadvantages since assumptions are usually difficult to justify, families of distributions contain too many parameters to be of practical use, and nonparametric methods make it difficult to characterize data in a succinct quantitative form. The S-distribution introduced here is a compromise between the conflicting goals of simplicity in analysis and generality in scope. It is characterized by four parameters, one of which reflects its location, the second one its spread, and the remaining two its shape; transformation to a standard form reduces the number of free parameters to two. Cumulatives and densities are computed numerically in fractions of seconds, key features like quantiles and moments are easily obtained, and results can be presented in terms of parameter values. The S-distribution rather accurately models different distribution functions, including central and noncentral distributions, and thus competes in flexibility with some distribution families. As an approximation, the S-distribution provides a graphical method for demonstrating relationships between distributions, such as the relationships between central F, χ² and χ^?2 or central and noncentral t, χ^-1, and normal.     

Potential Dry Matter and Water Import Rates in the Tomato Fruit in Relationship to Fruit Size

The tomato fruit was compared to a sphere with a radius R. Radialgrowth rates in the fruit (F_IW and F_ID) due to water importor to dry matter import, respectively, which are also the waterimport rate or dry matter import rate per unit surface areaof fruit, were calculated from two sets of published results.This data referred to fruits which swelled in such a way thatthe availability of assimilates had little effect on growth.Two varieties differentiated the two series of results and inone series, three trials were differentiated by the salinityof the nutrient solution. In all trials, it was found that F_IW and F_ID decreased whenR increased. Two phases were observed for F_IW: after a firstphase, F_IW decreased more quickly and almost linearly when Rincreased. F_ID was constant or decreased with respect to R.Except at the beginning of growth at the greatest salinity,there were clearly linear regressions between F_IW and F_ID suchas F_ID = aF_IW-b; where b was lower with higher salinity. Thechanges of the concentration of imported dry matter (F_ID/F_IWwere examined in terms of R and F_IW/R. The mechanisms controllingthe changes in F_IW and F_ID were discussed. The results suggestedfruit radius was an important parameter of these mechanisms.Thus, water import rate and dry matter import rate could eachbe considered to be the product of two factors: fruit surfacearea, which is directly dependent on fruit radius, and waterimport rate or dry matter import rate per unit of fruit surfacearea.Copyright 1993, 1999 Academic Press Dry matter, fruit growth, logistic model, sink size, tomato, water transfer     

The Method of Unweighted Means in Unbalanced Analysis of Variance

For factorial experiments with unbalanced data the method of unweighted means is an alternate method of analysis which is computationally simpler than likelihood ratio based F-tests. The quality of the null approximation to the F-distribution of the statistic for the method of unweighted means and the power of this test relative to the likelihood ratio test are discussed. Recommendations are made of when in the course of data analysis the superior operating characteristics of the likelihood ratio test may not outweigh the computational simplicity of the method of unweighted means test.     

Energy-Level Model for Isothermal Seed Germination

We have been successful in building an energy-level model thatdescribes seed germination. We used the autocatalytic reactionrate equation to fit the germination rate for seed germination.The two parameters [A]₀ and [F]₀ were found by fitting the integratedgermination rate equation to the data. The values of [A]₀ and[F]₀ obey the Arrhenius equation and give activation energiesfor the second and third stage of the four-compartmental modelof seed germination. The thermodynamics of isothermal seed germinationis proposed and the enthalpy, entropy, and free energy are calculatedfor the transition from state A to state F. The time delay isa function of temperature and it leads to a rate constant thatcan be used to get the activation energy for the total germinationprocess. We believe the model is universal. It fits alfalfa(Medicago sativa), turnip (Brassica rapa), and lettuce (Lactucasativa) seeds. Key words: Seed germination, thermodynamics, kinetics, Arrhenius, energy-level model     

Genetic Analysis of Growth in Tomato: Segregating Generations

Genetical control of certain aspects of plant development hasbeen studied in the segregating generations derived from a diallelcross involving three varieties of L. esculentum and one ofL. pimpinellifolium. In the first experiment, dry-weight relativegrowth-rate was found to be inherited additively with a largedominance component which, however, was probably overestimatedin the F₁ by the inclusion of only one type of reciprocal cross.Gene association in the parents was suggested by the distributionof the points in the diallel regression graph. In a second experiment,the increase in leaf number with time was followed in parental,F₁, F₂, F₃, and backcross generations. Genetical analysis forvarious parameters of rates of production of leaves showed thecontrol to be additive with various degrees of dominance, andsimilar results were found for analysis of results on time-to-floweringand fruit yields. There was, throughout the experiments, agreementbetween the results for each generation. It is believed thatcombined genetical and physiological studies of growth in cropplants will be of value in the selection of parents for breedingimproved varieties.     

Variation in EMG activity: a hierarchical approach

Recordings of naturally occurring Electromyographic (EMG) signalsare variable. One of the first formal and successful attemptsto quantify variation in EMG signals was Shaffer and Lauder's(1985) study examining several levels of variation but not withinmuscle. The goal of the current study was to quantify the variationthat exists at different levels, using more detailed measuresof EMG activity than did Shaffer and Lauder (1985). The importanceof accounting for different levels of variation in an EMG studyis both biological and statistical. Signal variation withinthe same muscle for a stereotyped action suggests that eachrecording represents a sample drawn from a pool of a large numberof motor units that, while biologically functioning in an integratedfashion, showed statistical variation. Different levels of variationfor different muscles could be related to different functionsor different tasks of those muscles. The statistical impactof unaccounted or inappropriately analyzed variation can leadto false rejection (type I error) or false acceptance (typeII error) of the null hypothesis. Type II errors occur becausesuch variation will accrue to the error, reducing power, andproducing an artificially low F-value. Type I errors are associatedwith pseudoreplication, in which the replicated units are nottruly independent, thereby leading to inflated degrees of freedom,and an underestimate of the error mean square. To address theseproblems, we used a repeated measures, nested multifactor modelto measure the relative contribution of different hierarchicallevels of variation to the total variation in EMG signals duringswallowing. We found that variation at all levels, among electrodesin the same muscle, in sequences of the same animal, and amongindividuals and between differently named muscles, was significant.These findings suggest that a single intramuscular electrode,recording from a limited sample of the motor units, cannot berelied upon to characterize the activity of an entire muscle.Furthermore, the use of both a repeated-measures model, to avoidpseudoreplication, and a nested model, to account for variation,is critical for a correct testing of biological hypotheses aboutdifferences in EMG signals.     

Expression of the nuclear gene TaF(A)d is under mitochondrial retrograde regulation in anthers of male sterile wheat plants with timopheevii cytoplasm

Alterations of mitochondrial-encoded subunits of the F_oF₁-ATPsynthase are frequently associated with cytoplasmic male sterility(CMS) in plants; however, little is known about the relationshipof the nuclear encoded subunits of this enzyme with CMS. Inthe present study, the full cDNA of the gene TaF_Ad that encodesthe putative F_Ad subunit of the F_oF₁-ATP synthase was isolatedfrom the wheat (Triticum aestivum) fertility restorer ‘2114’for timopheevii cytoplasm-based CMS. The deduced 238 amino acidpolypeptide is highly similar to its counterparts in dicotsand other monocots but has low homology to its mammalian equivalents.TaF_Ad is a single copy gene in wheat and maps to the short armof the group 6 chromosomes. Transient expression of the TaF_Ad–GFPfusion in onion epidermal cells demonstrated TaF_Ad's mitochondriallocation. TaF_Ad was expressed abundantly in stem, leaf, anther,and ovary tissues of 2114. Nevertheless, its expression wasrepressed in anthers of CMS plants with timopheevii cytoplasm.Genic male sterility did not affect its expression in anthers.The expression of the nuclear gene encoding the 20 kDa subunitof F_o was down-regulated in a manner similar to TaF_Ad in theT-CMS anthers while that of genes encoding the 6 kDa subunitof F_o and the subunit of F₁ was unaffected. These observationsimplied that TaF_Ad is under mitochondrial retrograde regulationin the anthers of CMS plants with timopheevii cytoplasm. Key words: CMS, F_Ad subunit, F_oF₁-ATP synthase, retrograde regulation, wheat Received 8 October 2007; Revised 9 January 2008 Accepted 28 January 2008     

Degrees of freedom in interspecific allometry: An adjustment for the effects of phylogenetic constraint

The data used in studies of bivariate interspecific allometry usually violate the assumption of statistical independence. Although the traits of each species are commonly treated as independent, the expression of a trait among species within a genus may covary because of shared common ancestry. The same effect exists for genera within a family and so on up the phylogenetic hierarchy. Determining sample size by counting data points overestimates the effective sample size, which then leads to overestimating the degrees of freedom that should be used in calculating probabilities and confidence intervals. This results in an inflated Type 1 error rate. Although some workers (e.g., Felsenstein [1985] Am. Nat. 125:1–15) have suggested that this issue may invalidate interspecific allometry as a comparative method, a correction for the problem can be approximated with variance components from a nested analysis of variance. Variance components partition the total variation in the data set among the levels of the nested hierarchy. If the variance component for each nested level is weighted by the number of groups at that level, the sum of these values is an estimate of an effective sample size for the data set which reflects the effects of phylogenetic constraint. Analysis of two data sets, using taxonomy to define levels of the nested hierarchy, suggests that it has been common for published studies of interspecific allometry to severely overestimate the number of degrees of freedom. Interspecific allometry remains an important comparative method for evaluating questions concerning individual species that are not similarly addressed by the format of most of the newer comparative methods. With the correction proposed here for estimating degrees of freedom, the major statistical weakness of the procedure is substantially reduced. © 1994 Wiley-Liss, Inc.     

Objective Bayesian analysis for the Student-t regression model

We develop a Bayesian analysis based on two different Jeffreyspriors for the Student-t regression model with unknown degreesof freedom. It is typically difficult to estimate the numberof degrees of freedom: improper prior distributions may leadto improper posterior distributions, whereas proper prior distributionsmay dominate the analysis. We show that Bayesian analysis witheither of the two considered Jeffreys priors provides a properposterior distribution. Finally, we show that Bayesian estimatorsbased on Jeffreys analysis compare favourably to other Bayesianestimators based on priors previously proposed in the literature.     

Effects of Seed Treatments on the Emergence of Oil Seed Rape Seedlings from Compacted Soil

Imbibition of seeds of oil seed rape (Brassica napus cv Jetneuf)in 10^–3 M aminoethoxyvinylglycine (AVG) or 10^–2silver thiosulphate (Ag⁺) had no effect on germination nor onthe emergence of seedlings from uncompacted or lightly compressedsoil, but significantly reduced emergence from moderately compressedsoil of 68.4 or 143.3 N cm^–2 impedance. Exertion of force by emerging control seedlings against a staticcantilever bar fitted with strain gauges reached a maximum (F_max)of 6 g over 10 h. Higher axial forces were achieved when theseedlings were emerging from compressed soil, without any changein the time required to reach F_max, so that the build-up offorce was considerably (1.8 fold) faster than in uncompressedsoil. This adaptive response to soil impedance was modified by theseed pretreatments employed. Seedlings from AVG or Ag⁺pretreatedseeds produced lower axial forces than controls, and neitherF_max nor the rate at which force developed showed any responseto soil compression. After pretreatment in 10^–3 ethephon or 10^–4 naphthaleneacetic acid (NAA) the seedlings achieved similar F_max to controlseedlings, but responded more rapidly to soil compression sothat the rate of build up of emergence force was 2.3 fold (NAA)or 2.8 fold (ethephon) faster in compressed than in uncompressedsoil. The results suggest that the exertion of force by a seedlingagainst a barrier involves a dynamic response to impedance onthe part of the seedling. This response can be either enhancedor suppressed by substances which affect ethylene productionor ethylene action. Such compounds may have promise for modifyingseedling emergence from impeding soils. Brassica napus, oil seed rape, seedling emergence, soil compaction, ethylene, Ethrel, silver, aminoethoxyvinylglycine, naphthalene acetic acid     

A Growth Analysis Technique for Assessing Habitat Severity in Tundra Regions

The results are reported of growth experiments carried out overthree seasons on the sub-Antarctic island of South Georgia.The values obtained for relative growth rate, net assimilationrate and leaf area ratio for oats, radish and turnip are discussedand contrasted with values reported for temperate sites. A hypothesisis put forward to explain the consistent depression of R^w andF^A whilst the intermittent depression of E^A is linked with WarrenWilson's theory of the inhibiting effects of sugar accumulation.The usefulness of this technique in ecological applicationsis examined with particular reference to tundra regions.     

Inhibition of growth and photosynthesis of freshwater phytoplankton by ultraviolet A (UVA) radiation and subsequent recovery from stress

The effect of ultraviolet A (UVA) on growth and photosyntheticrate was studied in diatoms (Melosira spp.) of the phytoplanktonof a eutrophic lake and a cultured green alga Chloretla ellipsoidea.The cells were incubated under photosynthetically active radiation(PAR) (–UVA) or PAR + UVA conditions (+UVA). Growth ofC.ellipsoidea was retarded under +UVA, as shown by an increasein the lag period, but the rate of exponential growth was almostthe same in + and –UVA conditions. The photosyntheticrate was depressed markedly by UVA in Chlorella cells grownunder –UVA. In contrast, cells grown in +UVA showed onlyslight inhibition by UVA and after exposure to UVA for 6 daysthere was no inhibition. During the growth experiment, the cellularchlorophyll a content was higher in +UVA than +UVA grown cells.A similar effect was observed in diatoms from the eutrophicLake Suwa. In vivo fluorescence with (F_a) and without 3-(3,4-dichloropheny)-l,l-dimethylurea (DCMU) (F_b) and the photosynthetic rate were measured forC.ellipsoidea and the diatoms for 5 h under + and –UVAconditions. Soon after C.ellipsoidea had been subjected to +UVA,F_b and F_a / F_b decreased quickly and reached minima after 40min and 1 h, respectively. The suppressed in vivo fluorescenceresumed and full recovery was achieved after 4 h. This suggeststhat reactivation of the photosystem is acquired under prolongedexposure to UVA. A similar shift of F_a + F_b, but no change inFb, was found in diatoms by exposure to UVA. Changes in photosyntheticoxygen evolution by C.ellipsoidea under +UVA were similar tochanges in F_a + F_b. Degradation of chlorophyll a extracted inmethanol was enhanced by UVA. The rate of degradation by UVAwas independent of temperature from 15 to 34°C, suggestinga photochemical reaction. The results indicate that C.ellipsoideaand Melosira spp. acclimatize to prolonged UVA exposure by reactivationof the photosystem and enhanced cellular chlorophyll a synthesis.The ecological importance of these results to phytoplanktonproductivity in natural aquatic environments is discussed.     

Effects of Seasonal Variation in Radiation and Temperature on Net Assimilation and Growth Rates in an Arid Climate

The net assimilation rate (E_A), relative growth-rate (R_w), andleaf-area ratio (F_A) were measured for rape (Brassica napus),sunflower (Hetianthus annuus), and maize (Zea mays) at varioustimes of year in an arid climate, using young plants grown widelyspaced on nutrient culture. Multiple regression analysis accountedfor 90–95 per cent of the variation in E_A and R_W in termsof two climatic variables: mean temperature and radiation receipt. E_A rose linearly with radiation in all three species; increasein E_A with temperature was greatest in maize and least (notsignificant) in rape. R_Wrose with radiation and temperature,the latter being the more important variable especially in coolweather; a temperature optimum was shown at 24° C in rape.F_A rose with increase in temperature or decrease in radiation;its variation was due to change in leaf area/leaf weight ratherthan in leaf weight/plant weight. Multiple regression analyses can lead to faulty interpretationif the independent variables are correlated (as are climaticvariables in nature), but conclusions can be checked by controlled-environmentstudies in which climatic factors are not correlated. The presentconclusions are supported by such studies. The regression equations, coupled with average weather records,indicate seasonal cycles of growth parameters. E_A is maximalnear midsummer and minimal near midwinter, following the radiationcycle. Maxima and minima in R_W are about a month later, becauseR_W is affected by the temperature cycle and this lags behindthe radiation cycle. F_A is maximal in autumn and minimal inspring. E_A is highest where radiation receipts near 750 cal cm^–2day^–1 coincide with high temperatures. This combinationoccurs only in clear midsummer weather at low latitudes, andis maintained over long periods only in arid regions. The fact that E_A rose linearly with radiation suggests thatleaf water deficits arising under high radiation had littleeffect on E_A and that saturating levels of light were very high.     

Sample Size Determination for Designing a Strata-Matched Case-Control Study to Detect Multiple Risk Factors

Investigations of sample size for planning case-control studies have usually been limited to detecting a single factor. In this paper, we investigate sample size for multiple risk factors in strata-matched case-control studies. We construct an omnibus statistic for testing M different risk factors based on the jointly sufficient statistics of parameters associated with the risk factors. The statistic is non-iterative, and it reduces to the Cochran statistic when M = 1. The asymptotic power function of the test is a non-central chi-square with M degrees of freedom and the sample size required for a specific power can be obtained by the inverse relationship. We find that the equal sample allocation is optimum. A Monte Carlo experiment demonstrates that an approximate formula for calculating sample size is satisfactory in typical epidemiologic studies. An approximate sample size obtained using Bonferroni's method for multiple comparisons is much larger than that obtained using the omnibus test. Approximate sample size formulas investigated in this paper using the omnibus test, as well as the individual tests, can be useful in designing case-control studies for detecting multiple risk factors.     

Sample preconditioning for measurement of fluorescence induction of chlorophyll a in marine phytoplankton

Conditions for measuring fluorescence induction curves (time-scalems) of in vivo chlorophyll ^a were studied using cultures ofDunaliella tertiolecta Butcher (Chlorophyceae) and of Thalassiosirapseudonana Hustedt (3H) (Bacillariophyceae), and samples ofnatural phytoplankton populations from the Grand Banks. Thearea above the fluorescence induction curve (A_DCMU) and themaximum fluorescence intensity (F_max) measured in the presenceof 3-(3,4-dichlorophenyl)-1, 1-dimethylurea (DCMU) were computedby microcomputer. Cells must be ‘conditioned’ or‘adapted’ prior to obtaining a fluorescence inductioncurve; dark-adaptation resulted in a lower A_DCMU and F_max thandid adaptation in far-red (720 nm) light, and was the conditioningmethod chosen. A_DCMU and F_max increased linearly with increasingirradiance up to 32.8 W m^–2 the highest actinic irradianceavailable. Information on the light history of D. tertiolectawas obtained by following the time-course of change in A_DCMUand in F_max for cells exposed for 10 min to far-red or to bluelight. The rise-time of the fluorescence induction curve andvalues of F_max were greater for samples of D. tertiolecta concentratedonto glass-fiber filters than for liquid samples, however, valuesof A_DCMU for filtered and liquid samples were not significantlydifferent. Samples of Grand Banks phytoplankton collected ontoglass-fiber filters and frozen for 28 d exhibited a significantdecrease in F_max and in A_DCMU relative to the same freshly-filteredsamples. Filtration and freezing of samples is not recommended. ^*This paper is the result of a study made at the Group for AquaticPrimary Productivity (GAP). Second International Workshop heldat the National Oceanographic Institute. Haifa. Israel in April–May1984.