Log Variance Research Articles

Wealth distribution and accounting for changes in wealth inequality: empirical evidence from India, 1991–2012

Despite its fast rise on the world stage and rapid economic growth, there has been a dramatic increase in wealth inequality in India in recent years. Nonetheless, the issue of wealth inequality and wealth distribution in India has been relatively less explored. In this context, we use an extension of Blinder–Oaxaca decomposition method based on the recentered influence function (RIF) proposed by Firpo et al. (Econometrics 6(2):28, https://doi.org/10.3390/econometrics6020028 , 2018) to analyze the role of household characteristics such as location, household’s composition by age, social groups, as well as education or employment on various wealth distributional measures during the period 1991–2012. We examine the effect of changing distribution of different household characteristics on wealth at various distributional measures (like ventile, Gini index, and variance). In our analysis, we observe the effect of household characteristics on wealth at different ventiles. Using counterfactual distribution analysis, we decomposed the inter-period difference in inequality into characteristics (explained) and coefficients (unexplained) effects. We then decompose changes in wealth at each ventile, Gini index, the variance of log of wealth, 90–10 percentile wealth gap, 50–10 wealth gap, and 90–50 wealth gap during 1991–2002 and 2002–2012 to see the composition effect and wealth structure effect. The composition effect shows the effect of change in the considered household characteristics, whereas the wealth structure effect shows the effect of change in returns to these characteristics. We noticed that during 1991–2002, wealth at lower quantile has decreased whereas it has increased for other quantiles, whereas during 2002–2012, we observe that wealth increase is highest at lower quantiles and is positive for all ventiles. In the case of inequality measures, we observe that all inequality measures have increased during 1991–2002, whereas during 2002–2012, only Gini and 90–50 gap has increased while other measures have decreased.

A guide on meta-analysis of time-to-event outcomes using aggregate data in vascular and endovascular surgery

BackgroundTime-to-event outcomes measure not only whether but also when an event happens. They are commonly used to evaluate vascular therapies, where the events of interest include disease recurrence (eg, loss of graft patency), reintervention (eg, target lesion revascularization), or death. Meta-analyses of published time-to-event outcomes are most appropriately measured by hazard ratios (HR). MethodsWe constructed a guide to increase awareness and adoption of these methods in vascular and endovascular surgery research, make systematic reviewers familiar with the basic principles of time-to-event data meta-analysis, and provide information about useful resources. ResultsCommonly, values of HR are not provided in published studies, but there are methods available to obtain such values and associated statistics from published summary data. Both direct and indirect methods can be applied to calculate the HR and its variance or standard error. Once individual study estimates of HR and its variance (or standard error) have been obtained, a pooled estimate of the log HR and variance can be calculated using the inverse-variance method. ConclusionsTime-to-event data should not be analyzed as dichotomous data. Such meta-analyses need to account for time and the differential censoring of the subjects. The HR is the preferred treatment effect measure. A mixture of direct or indirect methods can be applied to calculate the individual study estimates.

A probabilistic perspective on thermodynamic parameter uncertainties: Understanding aqueous speciation of mercury

Abstract Speciation plays an important role in determining the fate and transport of metals in terrestrial surface and subsurface systems. Equilibrium speciation modeling in aqueous systems relies on thermodynamic constants (log K values) of complexes, which are subject to uncertainties. Here, using Monte Carlo (MC) simulations with Latin hypercube sampling (LHS) we systematically analyze the propagation of thermodynamic constant uncertainty through speciation modeling of an inorganic mercury-sulfide-chloride-water system. We find that seemingly small variances of the input log K normal distributions can lead to output species concentrations spanning multiple orders of magnitude, with highly skewed probability distributions. When equilibrium with mineral metacinnabar (β-HgS(s)) is neglected, the relative uncertainty of each output species is strongly positively correlated with the skewness of its concentration probability distribution, i.e., the lowest uncertainty occurs when the species concentration probability distribution is the most negatively skewed as its concentration approaches the total element concentration limit. The highest uncertainty in the identity of dominant species is located around species equivalence points. For cases where the mineral equilibrium is included, we derive analytical probability density functions for the log concentrations of all major species in the system. The mineral log K uncertainty is found to be an important contributor to all output concentration uncertainties. The analysis of combined effects of both pH and total sulfide concentration on output concentration uncertainties shows that high concentration uncertainties occur under highly sulfidic alkaline conditions and low uncertainties at low pH and sulfide concentrations. An analysis as presented here can distinguish between conditions that require a full uncertainty analysis and those for which the classical deterministic speciation modeling suffices.

A New Design of Mental State Classification for Subject Independent BCI Systems

BackgroundBrain Computer Interface (BCI) systems have been widely used to develop sustainable assistive technology for people suffering from neurological impairments. A major limitation of current BCI systems is that they are based on Subject-dependent (SD) concept. The SD based BCI system is time consuming and inconvenient for physical or mental disables people and also not suitable for limited computer resources. In order to overcome these problems, recently subject-independent (SI) based BCI concept has been introduced to identify mental states of motor disabled people but the expected outcome of the SI based BCI has not been achieved yet. Hence this paper intends to present an efficient scheme for SI based BCI system. The goal of this research is to develop a method for classifying mental states which can be used by any user. For attaining this target, this study employs a supervised spatial filtering method with four types of feature extraction methods including Katz Fractal Dimension, Sub band Energy, Log Variance and Root Mean Square (RMS) and finally the obtained features are used as input to Linear Discriminant Analysis (LDA) classification model for identifying mental states for SI BCI system. ResultsThe performance of the proposed design is evaluated in several ways such as considering different time window length; different frequency bands; different number of channels. The mean classification accuracy using Katz feature is 84.35% which is the maximum output compare to other features that outperforms the existing methods. ConclusionsOur proposed design will help to make a new technology for development of real-time SI based BCI systems that can be more supportive for the motor disabled patients.

Proximate determinants of Taylor's law slopes.

Taylor's law (TL), a commonly observed and applied pattern in ecology, describes variances of population densities as related to mean densities via log(variance)=log(a)+b*log(mean). Variations among datasets in the slope, b, have been associated with multiple factors of central importance in ecology, including strength of competitive interactions and demographic rates. But these associations are not transparent, and the relative importance of these and other factors for TL slope variation is poorly studied. TL is thus a ubiquitously used indicator in ecology, the understanding of which is still opaque. The goal of this study was to provide tools to help fill this gap in understanding by providing proximate determinants of TL slopes, statistical quantities that are correlated to TL slopes but are simpler than the slope itself and are more readily linked to ecological factors. Using numeric simulations and 82 multi-decadal population datasets, we here propose, test and apply two proximate statistical determinants of TL slopes which we argue can become key tools for understanding the nature and ecological causes of TL slope variation. We find that measures based on population skewness, coefficient of variation and synchrony are effective proximate determinants. We demonstrate their potential for application by using them to help explain covariation in slopes of spatial and temporal TL (two common types of TL). This study provides tools for understanding TL, and demonstrates their usefulness.

Modeling of the Acute Lymphoblastic Leukemia Detection based on the Principal Object Characteristics of the Color Image

The objective of the research is to develop a model to detect the Acute Lymphoblastic Leukemia. This research contributes a model for Acute Lymphoblastic Leukemia Detection using Principal Object Characteristics of the Color Image. We developed method consist of four main stages as follows: enhancement, segmentation, feature extraction, and accuracy measurement. This research proposed seven characteristics as the object feature, which are Energy (EN), Entropy(EP), Shanon Entropy (H(X)), Log Energy Entropy (EE), Mean (ME), Variance (VA), and Correlation (CO). The feature extraction results have been calculated using four measurement methods, i.e. Euclidean Distance, Manhattan, Canberra, and Chebyshev methods. Our proposed method has produced maximum accuracy of 81.54%, 81.54%, 76.92%, and 82.31% for Euclidean Distance, Manhattan, Canberra, and Chebyshev methods, respectively. Lastly, we applied a confusion matrix to compute the accuracy of the experiment. Our proposed method has been evaluated using Acute Lymphoblastic Leukemia- Image Database (ALL-IDB).

Bortezomib-Based Consolidation/Maintenance Therapy for Multiple Myeloma: A Meta-Analysis of Randomized Controlled Trials

Background: Bortezomib is a proteasome inhibitor that can lead to cell-cycle arrest and apoptosis. Bortezomib-based regimens are widely used as induction therapy of multiple myeloma (MM). Unlike lenalidomide (an immunomodulatory drug), the role of bortezomib in the consolidation and maintenance therapy of multiple myeloma is less clear. This study aims to examine the efficacy and safety of bortezomib-based regimens as consolidation/maintenance therapy in MM patients following induction therapy with or without autologous stem cell transplantation (ASCT).Methods: PubMed, ASH, and ASCO databases were searched for randomized controlled trials (RTC) of bortezomib-based regimens (either single-agent or combination) as consolidation/maintenance therapy for MM patients through July 2018. Study endpoints included overall survival (OS), progression-free survival (PFS), and adverse events (AE). Pooled hazard ratios (HR) for survival outcomes and relative risks (RR) for dichotomous data with 95% confidence interval (CI) were calculated with a random effect model using MedCalc (MedCalc Software, Ostend, Belgium). For studies that did not report HRs for survival outcomes but provided graphical survival curves, the log HRs and variances were estimated based on the method by Parmar et al (Stat Med 1998; 17: 2815-2834). Heterogeneity was assessed using the I2 statistic of inconsistency, with statistically significant heterogeneity defined as I2 > 50% or p-value < 0.1.Results: Eight randomized controlled trials (7 phase III, 1 phase II; 2 were published in a single article) were identified. Bortezomib-based regimens were administered as consolidation treatment in 5 RTCs and maintenance therapy in 3 RTCs, following induction therapy +/- ASCT. A total of 2439 patients were included: 1154 patients received bortezomib-based regimens, and 1285 patients received non-bortezomib-based regimens or observation. Two RCTs (1 for consolidation, 1 for maintenance) did not provide HRs, which were estimated as described as above. Pooled data from the 8 RCTs showed that bortezomib-based consolidation/maintenance therapy improved progression-free survival (HR 0.71, 95% CI 0.64-0.79, P < 0.001; I2 = 6.61%) and overall survival (HR 0.80, 95% CI 0.68-0.94, P = 0.005; I2 = 0%) compared to observation or regimens without bortezomib. When the 2 RCTs that did not report HRs were excluded from the meta-analysis, it did not alter the favorable outcome of bortezomib-based consolidation/maintenance therapy: PFS (HR 0.70, 95% CI 0.60-0.82, P < 0.001; I2 = 40.54%) and OS (HR 0.76, 95% CI 0.64-0.91, P = 0.002; I2 = 0%). The PFS benefit was maintained in a subgroup analysis by the setting of treatment (consolidation, HR 0.73, 95% CI 0.63-0.85, P < 0.001; I2 = 0%, maintenance, HR 0.70, 95% CI 0.56-0.0.86, P = 0.001; I2 = 55.63%). Bortezomib-based therapy prolonged OS in the maintenance setting (HR 0.71, 95% CI 0.58-0.86, P < 0.001; I2 = 0%) but not in the consolidation setting (HR 1.01, 95% CI 0.77-1.33, P = 0.935; I2 = 0%). Regarding safety, bortezomib-based consolidation/maintenance therapy significantly increased the risk of grade 3 or 4 peripheral sensory neuropathy and neuralgia (RR 2.09, 95% CI 1.11-3.95, p = 0.022; I2 = 52.64%) compared to observation or regimens without bortezomib. There was a trend toward increased rates of grade 3 or 4 thrombocytopenia (RR 1.54, 95% CI 0.95-2.52, p = 0.08; I2 = 21.67%), GI symptoms (RR 2.54, 95% CI 0.63-10.25, p = 0.19; I2 = 76.72%), vascular events (RR 1.90, 95% CI 0.80-4.53, p = 0.15; I2 = 0.00%), and fatigue (RR 2.10, 95% CI 0.83-5.30, p = 0.12; I2 = 0.00%) with bortezomib-based consolidation/maintenance, but these did not reach statistical significance.Conclusions: Bortezomib-based consolidation/maintenance significantly improves PFS and OS in MM patients following induction therapy +/- ASCT. The OS benefit appears to be limited to the maintenance setting based on a subgroup analysis. Bortezomib-based regimen increases the risk of grade 3 or 4 peripheral sensory neuropathy and neuralgia. [Display omitted] DisclosuresBachanova:Gamida Cell: Research Funding; GT Biopharma: Research Funding; Kite Pharma: Membership on an entity's Board of Directors or advisory committees.

Firming Up Inequality*

AbstractWe use a massive, matched employer-employee database for the United States to analyze the contribution of firms to the rise in earnings inequality from 1978 to 2013. We find that one-third of the rise in the variance of (log) earnings occurred within firms, whereas two-thirds of the rise occurred due to a rise in the dispersion of average earnings between firms. However, this rising between-firm variance is not accounted for by the firms themselves but by a widening gap between firms in the composition of their workers. This compositional change can be split into two roughly equal parts: high-wage workers became increasingly likely to work in high-wage firms (i.e., sorting increased), and high-wage workers became increasingly likely to work with each other (i.e., segregation rose). In contrast, we do not find a rise in the variance of firm-specific pay once we control for the worker composition in firms. Finally, we find that two-thirds of the rise in the within-firm variance of earnings occurred within mega (10,000+ employee) firms, which saw a particularly large increase in the variance of earnings compared with smaller firms.

Comparing lethal dose ratios using probit regression with arbitrary slopes

BackgroundEvaluating the toxicity or effectiveness of two or more toxicants in a specific population often requires specialized statistical software to calculate and compare median lethal doses (LD50s). Tests for equality of LD50s using probit regression with parallel slopes have been implemented in many software packages, while tests for cases of arbitrary slopes are not generally available.MethodsIn this study, we established probit-log(dose) regression models and solved them by the maximum likelihood method using Microsoft Excel. The z- and χ2-tests were used to assess significance and goodness of fit to the probit regression models, respectively. We calculated the lethal doses (LDs) of the toxicants at different significance levels and their 95% confidence limits (CLs) based on an accurate estimation of log(LD) variances. We further calculated lethal dose ratios and their 95% CLs for two examples without assuming parallel slopes following the method described by Robertson, et al., 2017.ResultsWe selected representative toxicology datasets from the literature as case studies. For datasets without natural responses in the control group, the slopes, intercepts, χ2 statistics and LDs calculated using our method were identical to those calculated using Polo-Plus and SPSS software, and the 95% CLs of the lethal dose ratios between toxicants were close to those calculated using Polo-Plus. For datasets that included natural responses in the control group, our results were also close to those calculated using Polo-Plus and SPSS.ConclusionThis procedure yielded accurate estimates of lethal doses and 95% CLs at different significance levels as well as the lethal dose ratios and 95% CLs between two examples. The procedure could be used to assess differences in the toxicities of two examples without the assumption of parallelism between probit-log(dose) regression lines.

A simple method for combining binomial counts or proportions with hazard ratios for evidence synthesis of time-to-event data.

In studies with time-to-event data, outcomes may be reported as hazard ratios (HR) or binomial counts/proportions at a specific time point. If the intent is to synthesise evidence by performing a meta-analysis or network meta-analysis (NMA) using the HR as the measure of treatment effect, studies that only report binomial data cannot be included in the network. Methods for converting binomial data to HRs were investigated, so that studies reporting binomial data only could be included in a network of HR data. Estimating the log HR is relatively straightforward under the assumptions of proportional hazards and minimal censoring at the binomial data time point. Estimating the standard error of the log HR is harder, but a simple method based on using a Taylor series expansion to approximate the variance is proposed. Thus, we have 2 easy-to-calculate equations for the log HR and variance. The performance of the method was assessed using simulations and data from a NMA of multiple sclerosis treatments. In the simulation, our binomial method produced very similar HRs to those from survival analysis when censoring rates were low, and also when censoring rates were high but the event rate was low. In all situations, it outperformed using relative risk to approximate the HR. In the NMA, results were consistent between reported HRs and HRs derived from binomial data for studies that reported both types of data. This method may be useful for easily incorporating trials reporting binomial data into an evidence synthesis of HR data, under certain assumptions.

Forecasting realized variance measures using time-varying coefficient models

This paper considers the problem of forecasting realized variance measures. These measures are highly persistent estimates of the underlying integrated variance, but are also noisy. Bollerslev, Patton and Quaedvlieg (2016), Journal of Econometrics 192(1), 1–18 exploited this so as to extend the commonly used heterogeneous autoregressive (HAR) by letting the model parameters vary over time depending on the estimated measurement error variances. We propose an alternative specification that allows the autoregressive parameters of HAR models to be driven by a latent Gaussian autoregressive process that may also depend on the estimated measurement error variance. The model parameters are estimated by maximum likelihood using the Kalman filter. Our empirical analysis considers the realized variances of 40 stocks from the S&P 500. Our model based on log variances shows the best overall performance and generates superior forecasts both in terms of a range of different loss functions and for various subsamples of the forecasting period.

The Spatial Pattern of Aphis gossypii οn Cotton

The spatial distribution of Aphis gossypii (Glover) on cotton was studied by using Taylor’s power law, the negative binomial parameter k and the iδ-index of aggregation. Both k and iδ were related to density with curvilinear relationships and indicated that aggregation decreases as density increases up to densities of, approximately, two individuals per leaf. At the very high densities (more than three individuals per leaf) the calculated values of the two indices recognized a tendency for an increased aggregation again. A strong linear relationship between the log mean and the log variance of the population density was obtained confirming the wide applicability of Taylor’s power law. However, the established relationship (b=1.433) assumes, for the range of the observed densities, a continuous decrease in the degree of aggregation as density increases. It is suggested that the changes in the degree of aggregation throughout the season and in relation to density are related to natural mortality.

Validation of a Multiplexed Gene Signature Assay for Diagnosis of Canine Cancers from Formalin‐Fixed Paraffin‐Embedded Tissues

BackgroundUse of molecular‐based diagnostics for companion animals is impeded by availability of technology platforms, tissue acquisition requirements, and species‐specific reagents.Hypothesis/ObjectivesTo validate a quantitative nuclease protection assay (qNPA) to simultaneously measure RNA expression of multiple genes in archived formalin‐fixed paraffin‐embedded (FFPE) tumors from dogs.AnimalsAll tumor biopsy samples were collected retrospectively from surgical biopsies and in the care of veterinarians.MethodsRetrospective case series. A qNPA 96‐well ArrayPlate was built using 30 canine‐specific genes, 5 housekeeping genes, positive and negative controls with qualified gene‐specific oligonucleotides. Pearson's correlation, coefficient of variation (CV), and multivariate analysis were used to determine analytical performance using 40 FFPE dog tumors. Once validated, 70 FFPE dog tumors were analyzed for differences in gene expression using hierarchical clustering and analysis of variance of log transformed data. Immunohistochemistry (IHC) was performed to correlate gene expression and protein expression in a subset of tumors.ResultsThe assay was linear with decreasing sample input (R 2 = 0.978), reproducible within and between 96‐well plates (r = 0.988 and 0.95, respectively) and between different laboratories (CV = 0.96). Hierarchical cluster analysis showed grouping of tumors by histogenesis and oncogenes. Significant differences were found between BCl2, E2F transcription factor 1, MDM2, COX‐2, MET proto‐oncogene receptor kinase, and other biologically relevant gene expression in tumor subtypes. Immunohistochemistry confirmed protein expression.Conclusions and Clinical ImplicationsBecause this technology works reliably on FFPE specimens, it can help expedite the broad introduction of multiplexed genomic information for improved diagnostics and discovery of new targets for therapies in veterinary oncology.

Patterns of correlation of facial shape with physiological measurements are more integrated than patterns of correlation with ratings

This article exploits a method recently incorporated in the geometric morphometric toolkit that complements previous approaches to quantifying the facial features associated with specific body characteristics and trait attribution during social perception. The new method differentiates more globally encoded from more locally encoded information by a summary scaling dimension that is estimated by fitting a line to the plot of log bending energy against log variance explained, partial warp by partial warp, for some sample of varying shapes. In the present context these variances come from the regressions of shape on some exogenous cause or effect of form. We work an example involving data from male faces. Here the regression slopes are steepest, and the sums of explained variances over the uniform component, partial warp 1 and partial warp 2 are greatest, for the conventional body mass index, followed by cortisol and, lastly, perceived health. This suggests that physiological characteristics may be represented at larger scale (global patterns), whereas cues in perception are of smaller scale (local patterns). Such a polarity within psychomorphospace, the global versus the focal, now has a metric by which patterns of morphology can be modeled in both biological and psychological studies.

Spatial Patterns and Sequential Sampling Plans for Predators of Aphis glycines (Hemiptera: Aphididae) in Minnesota Soybean

The soybean aphid, Aphis glycines Matsumura, is an economically important soybean pest. Many studies have demonstrated that predatory insects are important in suppressing A. glycines population growth. However, to improve the utilization of predators in A. glycines management, sampling plans need to be developed and validated for predators. Aphid predators were sampled in soybean fields near Rosemount, Minnesota, from 2006-2007 and 2013-2015 with sample sizes of 20-80 plants. Sampling plans were developed for Orius insidiosus (Say), Harmonia axyridis (Pallas), and all aphidophagous Coccinellidae species combined. Taylor's power law parameters from the regression of log variance versus log mean suggested aggregated spatial patterns for immature and adult stages combined for O. insidiosus, H. axyridis, and Coccinellidae in soybean fields. Using the parameters from Taylor's power law and Green's method, sequential fixed-precision sampling plans were developed to estimate the density for each predator taxon at desired precision levels of 0.10 and 0.25. To achieve a desired precision of 0.10 and 0.25, the average sample number (ASN) ranged from 398-713 and 64-108 soybean plants, respectively, for all species. Resulting ASNs were relatively large and assumed impractical for most purposes; therefore, the desired precision levels were adjusted to determine the level of precision associated with a more practical ASN. Final analysis indicated an ASN of 38 soybean plants provided precision of 0.32-0.40 for the predators. Development of sampling plans should provide guidance for improved estimation of predator densities for A. glycines pest management programs and for research purposes.

Population dynamics, synchrony, and environmental quality of Hokkaido voles lead to temporal and spatial Taylor's laws.

Taylor's law (TL) asserts that the variance in a species' population density is a power-law function of its mean population density: log(variance)=a+b×log(mean). TL is widely verified. We show here that empirical time series of density of the Hokkaido gray-sided vole, Myodes rufocanus, sampled 1962-1992 at 85 locations, satisfied temporal and spatial forms of TL. The slopes (b±standard error) of the temporal and spatial TL were estimated to be 1.613±0.141 and 1.430±0.132, respectively. A previously verified autoregressive Gompertz model of the dynamics of these populations generated time series of density which reproduced the form of temporal and spatial TLs, but with slopes that were significantly steeper than the slopes estimated from data. The density-dependent components of the Gompertz model were essential for the temporal TL. Adding to the Gompertz model assumptions that populations with higher mean density have reduced variance of density-independent perturbations and that density-independent perturbations are spatially correlated among populations yielded simulated time series that satisfactorily reproduced the slopes from data. The slopes (b±standard error) of the enhanced simulations were 1.619±0.199 for temporal TL and 1.575±0.204 for spatial TL.

Detection and quantification of HIV-1 RNA with a fully automated transcription-mediated-amplification assay

BackgroundNucleic acid testing is the major method used to monitor HIV viral load. Commercial systems based on real-time PCR assays are available for high-volume centralized laboratory testing, but they are not fully automated. Objectives and study designWe have compared the diagnostic performance of the Hologic Aptima HIV-1 Quant Dx assay (Aptima) (based on real-time TMA) on the Panther instrument, a fully-automated random access platform, to that of, the Roche Cobas Ampliprep Cobas TaqMan (CAP/CTM) HIV-1 version 2.0 (based on real-time PCR). ResultsProbit analysis of replicate dilutions of NIBSC WHO International HIV-1 Standard, gave LODs of 8.6 c/ml for Aptima and 15.2 c/ml for CAP/CTM. The agreement between the assays was excellent when measuring HIV RNA in a calibrated reference (κ=0.90, p<0.001) and good when measuring clinical samples (κ=0.62, p<0.001). The correlation among the samples quantified by the two methods was very good (r=0.95, p<0.001) and the mean difference between the values obtained with the two assays was 0.02 log c/ml for B and non-B subtypes. The vast majority of results showed <0.5 log variance between the two assays (89%); only one sample showed results that differed by over 1.0 log c/ml. ConclusionThe performance of the new fully automated Aptima assay is adequate for clinical monitoring of HIV-1 RNA during infections and treatment. The Aptima assay is well suited for routine laboratory use.

Net Assimilation Rate Determines the Growth Rates of 14 Species of Subtropical Forest Trees.

Growth rates are of fundamental importance for plants, as individual size affects myriad ecological processes. We determined the factors that generate variation in RGR among 14 species of trees and shrubs that are abundant in subtropical Chinese forests. We grew seedlings for two years at four light levels in a shade-house experiment. We monitored the growth of every juvenile plant every two weeks. After one and two years, we destructively harvested individuals and measured their functional traits and gas-exchange rates. After calculating individual biomass trajectories, we estimated relative growth rates using nonlinear growth functions. We decomposed the variance in log(RGR) to evaluate the relationships of RGR with its components: specific leaf area (SLA), net assimilation rate (NAR) and leaf mass ratio (LMR). We found that variation in NAR was the primary determinant of variation in RGR at all light levels, whereas SLA and LMR made smaller contributions. Furthermore, NAR was strongly and positively associated with area-based photosynthetic rate and leaf nitrogen content. Photosynthetic rate and leaf nitrogen concentration can, therefore, be good predictors of growth in woody species.

Transformation Model Choice in Nonlinear Regression Analysis of Fluorescence-Based Serial Dilution Assays

Many modern serial dilution assays are based on fluorescence intensity (FI) readouts. We study the optimal transformation model choice for fitting five-parameter logistic curves (5PL) to FI-based serial dilution assay data. We first develop a generalized least squares-pseudolikelihood type algorithm for fitting heteroscedastic logistic models. Next, we show that the 5PL and log 5PL functions can approximate each other well. We then compare four 5PL models with different choices of log transformation and variance modeling through a Monte Carlo study and real data. Our findings are that the optimal choice depends on the intended use of the fitted curves. Supplementary materials for this article are available online.

Laplace Variational Approximation for Semiparametric Regression in the Presence of Heteroscedastic Errors

Variational approximations provide fast, deterministic alternatives to Markov chain Monte Carlo for Bayesian inference on the parameters of complex, hierarchical models. Variational approximations are often limited in practicality in the absence of conjugate posterior distributions. Recent work has focused on the application of variational methods to models with only partial conjugacy, such as in semiparametric regression with heteroscedastic errors. Here, both the mean and log variance functions are modeled as smooth functions of covariates. For this problem, we derive a mean field variational approximation with an embedded Laplace approximation to account for the nonconjugate structure. Empirical results with simulated and real data show that our approximate method has significant computational advantages over traditional Markov chain Monte Carlo; in this case, a delayed rejection adaptive Metropolis algorithm. The variational approximation is much faster and eliminates the need for tuning parameter selection, achieves good fits for both the mean and log variance functions, and reasonably reflects the posterior uncertainty. We apply the methods to log-intensity data from a small angle X-ray scattering experiment, in which properly accounting for the smooth heteroscedasticity leads to significant improvements in posterior inference for key physical characteristics of an organic molecule.