Calculation Of Standard Errors Research Articles

Overview of a Passive Tracking Index for Monitoring Wild Canids and Associated Species

Population density estimates for many animal species are often difficult or expensive to obtain, and they rely on assumptions that, if violated, result in unmeasurable estimation errors. Density estimates also may be unnecessary for research or management purposes, because an index that tracks changes in a population within appropriate time and geographic constraints could provide the information necessary to make management decisions or to evaluate the impact of a control program. We review research on a passive tracking index where observations are made on a series of tracking plots placed on lightly used dirt roads. The number of sets of tracks (individual intrusions) are recorded for each species of interest on each plot on consecutive days. The mean number of intrusions over the plots is calculated for each day for each species. The index is the mean of the daily means. These design and measurement methods present valuable advantages over most traditional tracking plot methods. Because no scents or baits are used as attractants, no conditioning of animals to the plots biases the results. This also permits multiple species, predator and prey alike, to be simultaneously monitored. Using the number of animal intrusions as observations produces results that are far more sensitive to change than tracking surveys where only presence or absence of spoor are recorded for each plot. Of particular importance, the statistical properties inherent to this data structure permit calculation of standard errors, confidence intervals and statistical tests, without subjectively subdividing the data.

Latent Transition Modeling of Progression of Health-Risk Behavior

Longitudinal studies are helpful for understanding the complex progression of health-risk behavior over time and for identifying risk factors amenable to intervention. This article focusses on methods for modeling transitions between health-risk states over time when .are common multiple indicators of health-risk are available. Multiple measures of health-rick in studies which utilize questionnaires and surveys involving a series of self-report questions ach providing information regarding health-risk. A latent transition model is presented as am alternative to approaches that analyze indicators separately or use summative indices. These approaches ignore both the correlation between indicators and the multidimensional structure of health-risk. In the present article, transitions between latent health-risk states are modeled using a logistic regression model for nominal responses. A two-stage estimation procedure which is an estimating equations analogue of the pseudo-likelihood method is applied so that the complexity of full maximum likelihood is avoided and standard error calculation is straightforward. This procedure is applied to self-report data on weapons carrying behavior in an urban sample of schoolchildren followed annually for five years.

Formula Bias and Within-stratum Substitution Bias in the U.S. CPI

In 1978 BLS adopted an estimator for U.S. CPI component indexes that incorporates scientific samples of outlets and varieties and that allows the calculation of reliable standard errors. Consumer substitution of outlets and varieties offering better values could cause bias in these indexes. A more important source of bias is, however, a tendency to give excessive weight to items whose initial price is temporarily low. The empirical evidence is striking. Average price series and matched food CPIs grew at almost the same rate before 1978, but between 1980 and 1992 the CPIs average about 1.4% per year more growth. For unleaded gasoline, the discrepancy averages 0.8% per year.

Driver choice of parking in the city

Of relevance to urban transportation planning in a scenario studied here are the choices of 5000 motorists among 55 parking lots and garages when travelling to one of 13 destinations in a city. These people behave as if they were minimizing a linear combination of driving distance, walking distance and parking fee. Walking is six times more costly than driving. Multi-level garages directly connected to a destination point have a special attraction equivalent to four normal parking facilities. Also influencing driver choice is a random element with a standard deviation of 400 m of walking. None of these factors is significantly affected by parking duration. Estimators that maximize the logarithm of the likelihood function have been determined by non-linear optimization techniques. Calculation of standard errors has been modified to accommodate a lack of statistical independence between the results for different payment periods or walking destinations. Computing charges were reduced 97%, with negligible effect on accuracy by temporarily replacing the probit by the logit model during a preliminary analysis of the data.

Pseudo-likelihood estimation for a class of spatial Markov chains

We consider a class of finite state, two-dimensional Markov chains which can produce a rich variety of patterns and whose simulation is very fast. A parameterization is chosen to make the process nearly spatially homogeneous. We use a form of pseudo-likelihood estimation which results in quick determination of estimate. Parameters associated with boundary cells are estimated separately. We derive the asymptotic distribution of the maximum pseudo-likelihood estimates and show that the usual form of the variance matrix has to be modified to take account of local dependence. Standard error calculations based on the modified asymptotic variance are supported by a simulation study. The procedure is applied to an eight-state permeability pattern from a section of hydrocarbon reservoir rock.

Sampling surficial fluvial gravels; the precision of size distribution percentile sediments

ABSTRACT Grid-by-number (Wolman) sampling is commonly used to characterize the texture of surficial fluvial sediments. Assessments of sampling precision have concentrated on the median grain size, but adequate representation of other grain size percentiles is paramount in a number of sedimentological contexts. The field effort required to construct percentile sampling distributions by replication is prohibitive, and the absence of any general size distribution for fluvial sediments precludes theoretical calculation of percentile standard errors. Bootstrapping is used in this paper to determine percentile standard errors for large samples from two gravel bar surfaces. The improvement of percentile precision with sample size follows the theoretical expectation, hence improvement in percentile recision is achieved only at the expense of much greater sampling effort once sample sizes reach about 400 stones. However, absolute percentile standard errors differ significantly from theoretically derived values. Of particular interest is the stability of coarser percentile estimates in coarse-skewed distributions; D95 estimates may be as precise as D50 estimates for a given sample size. The sensitivity of the precision of estimated percentiles to distribution shape is examined using synthetic skewed and bimodal grain size distributions. The absolute precision of percentile estimates is shown to vary with the grain size distribution of a particular sediment. Our field results provide a reference for further work.

APPLIED USE OF MIXED MODEL VS FIXED MODEL ANALYSIS IN FIELD RESEARCH

Statistical analysis of agricultural research has traditionally been via the use of fixed model methods. However, recent advances in statistical software have made analysts through random or mixed model methods more practical. Errant or inappropriate use of statistical programs to analyze data has been a recurring problem in the reporting of agricultural research findings. Often variables are all considered to be fixed in order to facilitate analysis, when in reality some variables in field research are nearly always random. Proper selection of error terms and calculation of standard errors are also frequently done incorrectly when statistical analysts packages are not used correctly. Unbalanced data is also quite normal in field research due to unforseen circumstances that result in lost information. Most of these situations can be more early handled with a mixed model approach. In this work, a broccoli field trial involving tillage and planting dates was analyzed using the General Smear Models procedure in SAS and the General Elmer Mixed Models Procedure in GLMM. Comparison of the analyses revealed that conclusions would differ somewhat with balanced data and even more with unbalanced data. Since variance components from all random effects are used to calculate standard errors in GLMM, standard errors in the mixed model were larger, but likely more accurate Inference space was also broader and allowed prediction space to include the entire population of experimental units which were sampled in the experiment. The mixed model procedure was more efficient and thus more sensitive to differences in treatments.

PREDICTION OF BREEDING VALUES FOR UNMEASURED TRAITS FROM MEASURED TRAITS

Henderson (1977, 1984) described a method for prediction of breeding values for traits not in the model for records. This method may be practical for animal or sire models for the case when no measurements can be obtained on any animals for some traits to be evaluated. The least squares equations are augmented with A-1⊗GN-1 rather than with A-1⊗G0-1 where A is the numerator relationship and G0and GN are the genetic covariance matrices for measured and for all traits. This method can be used for each unmeasured trait or simultaneously for measured and all unmeasured traits. An option in the MTDFRUN module of the Multiple Trait Derivative Free REML (MTDFREML) program of Boldman et al. (1993) is to obtain solutions for breeding values and their prediction error variances. However, the preparation program (MTDFPREP) must be tricked to set-up equation numbers for breeding values of the unmeasured traits. Adding dummy records for the unmeasured traits but with missing records for the measured traits for dummy animals to the data file of animals with measured traits but with missing unmeasurable traits will result in the needed equations. At least two dummy records are needed to avoid a divide by zero error in calculating the sample standard deviation. The dummy records need to be associated with a level of at least one fixed factor. The dummy animals also must be added to the pedigree file with unknown sires and dams before running the program to obtain the inverse of the numerator relationship matrix (MTDFNRM). In the program to obtain solutions to the multiple trait mixed model equations (MTDFRUN), the full genetic (co)vaiiance matrix, GN, for both measured and unmeasured traits is needed. The residual (co)variance matrix must have zero covariances between pairs of measured and unmeasured traits but the variance of the unmeasured trait must not be zero. This procedure provides direct solutions for breeding values of unmeasured traits based on mixed model predictions of breeding values of the measured traits and also allows calculation of standard errors of prediction for the solutions directly from elements of the inverse of the ugmented coefficient matrix. For example, this procedure can be used to predict breeding values of bulls (which have tenderness measurements) for the correlated trait of tenderness as a steer or heifer which cannot be measured on the bull.

On the calculation of standard error for quotation in confidence statements

The variability of a parameter estimator θ is often expressed by quoting, within parentheses, a value of standard error, say σ . Typically the latter is calculated via an asymptotic formula, or by application of the bootstrap or jackknife. A common interpretation of the quotation “ θ ( σ )” is that the confidence interval I = ( θ − 2 σ , θ covers the true value of θ with probability approximately 0.95. However, in problems where the allowable range of θ is sharply restricted by the context it is sometimes the case that one or other of the endpoints of I lies outside the allowable range. This happens because information about the allowable range is not adequately taken into account when computing the standard error. Examples include confidence statements about ratios of means. In the present paper we suggest a remedy for this problem. We propose a new, symmetrized version of Owen's empirical likelihood method, and use it to construct range-respecting, symmetric confidence intervals. These intervals suggest new formulae for standard error. An alternative approach may be based on a version of the bootstrap, although the latter is more expensive in computing time.

Modelling the yellowfin tuna (Thunnus albacares)vertical distribution using sonic tagging results and local environmental parameters

Resume Cayre P., F. Marsac. Aquat. Lining Resour., 1993, 6, 1-14. The diurnal vertical behaviour of yellowfin tuna observcd from sonic tagging experimcnts in the western Indian Ocean (Comoros archipclago) is compared with thc vertical profiles of temperature and dissolved oxygen conccntration. Two different behavioural situations: off-FAD and FAD-associated yellowfin tuna, are characterized by the relationships between swimming depth and vertical structure of temperaturc and dissolved oxygen conccntration (Le. depth and thickness of the mixed layer, of the thermocline layer and of the oxycline) observed in thc tracking area. Gradients of both paramelers are shown to be the key factors which determine the vertical swimming bchaviour. From an analysis carried out on the whole oceanographic data set of the Western Indian Ocean, oxyclinc is found to match with the depth of the 4.2-4.3 ml. 1- ' dissolved oxygen concentration. Vertical distributions of yellowfin tuna, for both off-FAD and FAD-associated situations, are modelled by using normal-derived distributions. These models indicatc the probability of the presence of yellowfin tuna, related to the vertical profiles of temperature and dissolved oxygen concentration. A single mode distribution is fittcd to describe the FAD-associated situation, and a bi-modal one for the off-FAD situation. Positions of the modes are determined by the relationship between the vertical swimming behaviour and the position of either maximum gradient of temperature or dissolved oxygen concentration. An iterative calculation of normal distribution standard error is conducted to adjust the shape of the eurve to cover the entire layer in which yellowfin tuna is considercd to be present. Both models were applicd in a remote area, east of the Seychelles, where purse seine catches are important. The predicted vertical distribution seems to be realistic and matchcs the observations given by echosound pictures of tuna schools obtained in the same area by purse seiners.

Statistical aspects of earthquake source parameter estimation in the presence of signal generated noise

Seismologists have developed models which relate observed ground motion to the physical parameters of the earthquake which caused it These models are based on an idealized model which approximates the behavior of the real earth. In this paper we will examine some of the uncertainties which cause observations to deviate from such models. These uncertainties include presence of contaminating noise and the wave scattering caused by the inhomogeneous nature of the earth. By modeling such uncertainties statistically, we are able to formulate a maximum -likelihood type procedure for model fitting and address the such issues as of the computation of standard errors and graphical diagnostics for goodness-of-fit. The paper illustrates the procedure on observations from a small Califomian earthquake.

Codend selection in American plaice: diamond versus square mesh

Codend selection in American plaice, (Hippoglossoides platessoides), was studied using the trouser trawl method. Mesh selection studies were carried out using 130 mm, 140 mm and 155 mm diamond and square mesh codends in experiments off the east coast of Canada in 1988 and 1990. Selection curves and selection parameters were calculated using a modified logistic model which allows for calculation of standard errors. The split of fish into the two codends (large mesh and small mesh) was estimated and tested for significant departure from the 50:50 split assumption in trouser trawl catches. Fifty percent retention lengths and selection factors were higher for diamond mesh codends than square mesh codends, implying that square mesh retains more smaller American plaice than diamond mesh codends. The implication of introducing square mesh codends in a mixed fishery is discussed.

Computation of Standard Errors for Geary-Khamis Parities and International Prices: A Stochastic Approach

Computation of Standard Errors for Geary-Khamis Parities and International Prices: A Stochastic Approach

Efficiency of robust standard errors for regression coefficients

The standard errors of least squares regression coefficients can be estimated in such a way as to be robust to heteroscedasticity of errors. The possible inefficiency of these robust standard errors is investigated and illustrated. A compromise standard error calculation, based on local smoothing of squared residuals, is also analyzed.

Estimation of parasitic infection dynamics when detectability is imperfect

The simultaneous estimation of infection rate, cure rate and detectability of parasitic infections is considered. A new method for this estimation based on a simple statistical model assuming constant transition rates between parasite states is proposed. Repeated observations on the infection status of the same individuals is required for this method. A maximum likelihood approach is used for parameter estimation and the calculation of standard errors of the estimates. The method is illustrated by a longitudinal study of the presence of Giardia lamblia infection in Kenyan children.

Price elasticities from survey data: Extensions and Indonesian results

This paper extends and improves the author's earlier work on measuring own- and cross-price elasticities from spatial variation in prices using household survey data. Double-logarithmic demand functions are replaced by functions that relate budget shares to the logarithms of prices and incomes, and zero expenditures are treated appropriately. Formulae are developed for estimation and for the calculation of standard errors. Limited Monte Carlo evidence suggests that the asymptotic approximations work well in practice. An eleven–commodity system of food demands is estimated using Indonesian data from 1981.

Model Estimation when Observations are not Independent:

Parameter estimation and the computation of standard errors in social science models often require the assumption that observations are independent. This assumption is frequently violated with pooled cross-section and time-series data and household survey data. A recent article by Liang and Zeger (1986) shows that classical estimation methods retain good statistical properties in a wide variety of analyses where observations are not independent, and that correct standard errors of estimated model parameters are not difficult to compute. This article describes one of Liang and Zeger's results and presents its applications to the estimation of linear and logistic regression models from pooled cross-section and time-series data.

Modification of sr 2508 sensitization in hypoxic V79 cells by manipulation of glutathione levels

This series of experiments employed the hypoxic cell sensitizer SR 2508 in concentrations ranging from 0.1 to 10 mM and V-79 cells irradiated in air or made hypoxic in glass syringes, then irradiated with 15 MV X rays. Using a series of survival curves measured at the various concentrations, K curves relating sensitizer enhancement ratio (SER) to SR 2508 concentration were calculated with normal GSH levels or with depletion of GSH to 0% using 1 mM buthionine sulfoximine (BSO) or elevation to 200% of normal using 1 mM oxothiazolidine carboxylate (OTZ). Survival curves were fitted by computer, allowing calculation of standard errors for the SER values. The depletion of GSH by BSO sensitized hypoxic and aerated cells significantly and caused more than additive enhancement of SR 2508 sensitization in hypoxic cells. Elevation of GSH with OTZ protects cells irradiated in air or hypoxia and reduces the SER obtained with SR 2508. The results further support the importance of GSH levels in influencing sensitization by nitroimidazoles.

Standard error calculations for non-seasalt constituents in marine precipitation

Pollutant transport studies and investigations of geochemical cycling often involve calculation of excess (non-seasalt) concentrations for various ions found in precipitation. Excess concentrations are calculated from measurements of the concentrations of a reference species and the species of interest. Formulas for determining the accuracy of calculated excess concentrations are necessary because this accuracy can vary significantly from sample to sample within the same data set, as well as from one study to another. The formulas derived in this paper demonstrate that the standard error of calculated excess concentrations is dependent on the nature and magnitude of the analytical errors made in measuring total concentrations. Application to a real data set indicates that this standard error is often greater than the calculated excess concentration, and that the standard error may vary by orders of magnitude for various samples in the same data set. The magnitude of the potential errors has important implications for the reliability of conclusions based on calculated excess concentrations, while the sample-to-sample variation of these errors complicates the process of determining the accuracy of summary statistics such as the volume-weighted mean concentration. In addition, these variations in accuracy can obscure the relationships between excess concentrations and other variables, both chemical and meteorological. This complicates investigations of source-receptor relationships and geochemical cycling, and may lead to faulty conclusions.

Direct identification of parameters in a mathematical model describing conduction through the atrioventricular node

Function of the atrioventricular node is assessed during intracardiac electrophysiology study by relating the output intervals A 2 H 2 and H 1 H 2 to the input A 1 A 2, where A and H are, respectively, atrial and His bundle electrograms recorded by catheter. The H 1 H 2 curves have been previously deduced from a model describing the A 2 H 2 curves. Because of presence in a few cases of different behaviour of A 2 H 2 and H 1 H 2, this study aimed to establish a more suitable model of H 1 H 2 independently of A 2H 2 for the particular case of a single transmission pathway. The two models were compared by calculation of standard error of the estimate. As a firt approximation, the deduced model may be sufficient. However, the standard error of the estimate was less with the direct algorithm, which is therefore the more suitable for further development, particularly for recognition and modelling of conduction over multiple pathways through the atrioventricular node.