Fractional Replication Research Articles

“Fractional replication” in single‐visit multi‐season occupancy models: Impacts of spatiotemporal autocorrelation on identifiability

Abstract Understanding variation in species occupancy is an important task for conservation. When assessing occupancy patterns over multiple temporal seasons, it is recommended to visit at least a subset of sites multiple times within a season during a period of closure to account for observation biases. However, logistical constraints can inhibit re‐visitation of sites within a season, resulting in the use of single‐visit multi‐season occupancy models. Some have suggested that autocorrelation in space and/or time can provide “fractional replication” to separately estimate occupancy probability from detection probability, but the reliability of such approaches is not well understood. We perform an extensive simulation study to assess the reliability of estimates from single‐visit multi‐season occupancy models under differing amounts of spatial and temporal autocorrelation (“fractional replication”). We assess model performance under both correctly specified models and multiple forms of model mis‐specification, and compare estimates from single‐visit models to models with varying amounts of within‐season replication. We also assess the reliability of single‐visit models to estimate occupancy probability of ovenbirds (Seiurus aurocapilla) in New Hampshire, USA. We found less bias in estimates from single‐visit occupancy models with long‐range spatial autocorrelation in occupancy probability compared to short‐range spatial autocorrelation when the model is correctly specified. However, under certain forms of model mis‐specification, estimates from single‐visit multi‐season occupancy models were biased and had low coverage rates regardless of the characteristics of the “fractional replication”. In contrast, models with varying amounts of additional replication were robust to model mis‐specification. Our findings suggest that “fractional replication” cannot replace true replication in terms of occupancy probability identifiability and that researchers should consider the potential inaccuracies when using single‐visit multi‐season occupancy models. We show that a little true replication can go a long way with even 10% of sites being revisited within a season leading to reasonably robust estimates even in the presence of extreme model mis‐specifications. When possible, we recommend performing multiple within‐season visits to at least a subset of spatial locations or integrating single‐visit data with other data sources to mitigate reliance on parametric assumptions required for reliable inference in single‐visit multi‐season occupancy models.

An Experimental Comparison of the Impact of 'Warning' and 'Health Star Rating' FoP Labels on Adolescents' Choice of Breakfast Cereals in New Zealand.

This research investigated the performance of the red, octagonal Vienna Convention traffic ‘STOP’ sign as a front of pack (FoP) warning nutritional label. While the Vienna Convention traffic light system is an established FoP label, the potential of the ‘STOP’ sign in the role has not been investigated. The performance of the ‘STOP’ label was compared with that of a single star (low nutritional value) Australasian Health Star Rating (HSR) label using a fractionally replicated Latin square design. The labels were presented on choice diads of cold breakfast cereal packets. The sample of 240 adolescents aged 16–18 was drawn from a secondary school in the South Island of New Zealand. A large and significant main effect was observed at the p < 0.01 level for the difference between the ’STOP’ sign and the control condition (no nutritional FoP label), and at p < 0.05 for the difference between the HSR and the ‘STOP’ label. There was no significant difference between the HSR FoP and the control condition. A significant non-additivity (interaction) (p < 0.01) was also observed via the fractional replication. The results indicate that the Vienna Convention ‘STOP’ sign is worthy of further research with regard to its potential as an FoP nutritional label.

Systematic Image Zooming and Panning of Graphical Images Using Fractional Replication

Scaling is the major operation performed in Transformation of images. The Scaling is an important operation for resizing and reshaping the images that are in digital form. Various operations can be performed with digital images out of which the shrinking and zooming are the most widely operations by any type of users in the world. The other name for shrinking is sub sampling and the zooming operation is also named as Oversampling. The purpose of zooming operation is to extend or enlarge the image in order to have a clear and efficient view. Zooming operations are mostly performed in our mobile for viewing the images in our gallery and this operation is the most frequently performed operation by the mobile users. By considering all these factors, graphical images are the most widely agent to convey any information to the transmitter in order to know the position, size of an object. With this in concern, we try to focus on graphical image zooming as it is very important process in image processing. In this paper, we have used Fractional Replication for Image Zooming that is processed by copying and replicating the pixels from the base image based on the inexact spatial correspondence between the base image and zoom image. And also, the pixel address of the zoom image is calculated fractionally from the pixel address of the base image. We have implemented all the zooming operations like Zoom out in subject of Y-Axis, Zoom out in subject of X-Axis, Zoom in subject of Y Axis, Zoom in subject of X Axis, Left Side Panning, Right Side Panning, Top Zoom Panning and Bottom Zoom Panning for a graphical image using C programming language. Here we attempt to process the various Zooming operation analysis of the graphical image.

Research on the possibilities of using linear observation models in welding processes

The usage relevance of linear observation models of welding processes is substantiated. A brief analytical review of scientific papers on using linear observation models for researching the processes of arc welding is introduced. An example of studies utilizing a linear observation model based on the results of experiments with alloying of a weld metal is given. The type of linear observation model – fractional replication – is determined. An experiment planning matrix and test results are given. After performing tests and processing the experimental data, mathematical models in the form of dependencies of the transfer of alloying elements into the weld metal were obtained. According to the results of the experiments, empirical models in the form of dependencies evaluating the percentages of manganese, silicon and carbon, transfer coefficients from the “wire-to-product” distance, the diameter of the welding nozzle and the filling wire feed rate were obtained. Since the degree of uncertainty of parameters during welding is high enough, the necessity of further modification of linear observation models using expert knowledge is justified. The mathematical specification of the linear observation model with parameters in the form of fuzzy intervals is given. An algorithm for identifying the parameters of a linear observation model in the form of fuzzy intervals has been developed.

FREP: Energy proportionality for disk storage using replication

Energy saving has become a crucial concern in datacenters as several reports predict that the anticipated energy costs over a three year period will exceed hardware acquisition. In particular, saving energy for storage is of major importance as storage devices (and cooling them off) may contribute over 25 percent of the total energy consumed in a datacenter. Recent work introduced the concept of energy proportionality and argued that it is a more relevant metric than just energy saving as it takes into account the tradeoff between energy consumption and performance. In this paper, we present a novel approach, called FREP (Fractional Replication for Energy Proportionality), for energy management in large datacenters. FREP includes a replication strategy and basic functions to enable flexible energy management. Specifically, our method provides performance guarantees by adaptively controlling the power states of a group of disks based on observed and predicted workloads. Our experiments using a set of real and synthetic traces show that FREP dramatically reduces energy requirements with a minimal response time penalty.

Investigating the Use of Fractional Replication and Taguchi Techniques in Cryopreservation: A Case Study Using Orthodox Seeds of a Tropical Rainforest Tree Species

Cryopreservation is increasingly important for conserving endangered species including tropical rain forest germplasm where optimal cryopreservation protocols must be established rapidly sacrificing little germplasm. Currently, full factorial experiments analysed by ANOVA establish optimal conditions. However, these experiments can contain many treatment combinations whilst ANOVA identifies significant effects without guaranteeing to find robust optimal conditions. Taguchi optimization techniques efficiently identify robust conditions through fractional factorial experiments with an appropriate signal to noise ratio (SNR). This paper reports for the first time the use of Taguchi techniques in cryopreservation. An orthodox seed (Cassia siamea Lam.) was used to guarantee sufficient data to compare full and fractionally replicated experiments analysed using both ANOVA and SNR. For sprouting day (smaller is better), identical significant main effects were found for all experimental sizes for ANOVA and SNR. The 1/4 replicate did not allow investigation of interaction terms, but the significant main effects were the same for larger experiments. For shoot to root ratio (nominal is best), a significant main effect was found for all experimental sizes using ANOVA. This was also found using SNR, which identified additional significant main effect and interactions. No significant effects were found for dry weight (larger is better). We show smaller experiments are possible, provided important two level interactions are analysed. Differences determining the optimal treatment combination were found between ANOVA and SNR; with the Taguchi choice provides more robust solutions. Taguchi optimization techniques are recommended when germplasm is scarce and/or the experiment needs to be conducted rapidly.

Effect of Particle Size and Moisture Content on Viscosity of Fish Feed

ABSTRACTA model was developed for the influence of particle size on the extrusion of a fish feed and the physical characteristics of the extrudates evaluated. The study was conducted using factorial experiments in a fractional replication design for four variables with three levels, and one‐third of the replicates (34 factorial in 27 units) were examined in a laboratory extruder. The torque‐screw speed measurement was used to develop a viscosity model equation that considered different shear rates, product temperature, initial moisture content, and particle size. When particle size decreased, the apparent viscosity became smaller. The barrel pressure was important in producing extrudate with a uniform volume over the range of processing conditions tested because it had a strong correlation with the volumetric expansion. The material with lower moisture and larger particles caused the specific mechanical energy to increase. The viscosity model developed in this study can be applied to the development of large‐scale extrusion models that determine the effect of particle size on the feed material extrudates.

The Design of Experiments: Statistical Principles for Practical Application

Preface Part I. Overture: 1. Introduction 2. Elementary ideas of blocking: the randomised block design 3. Elementary ideas of treatment structure 4. General principles of linear models for the analysis of experimental data 5. Computers for analysing experimental data Part II. First Subject: 6. Replication 7. Blocking 8. Multiple blocking systems and cross-over designs 9. Randomisation 10. Covariance - extension of linear models 11. Model assumptions and more general models Part III. Second Subject: 12. Experimental objectives, treatments and treatment structures 13. Factorial structure and particular forms of effects 14. Split unit designs and repeated measurements 15. Incomplete bloxk size for factorial experiments 16. Some mathematical theory for comfounding and fractional replication 17. Quantitative factors and response functions 18. Response surface exploration Part IV. Coda: 19. Designing useful experiments References Index.

On screening samples in the laboratory and factors in factorial investigations

Procedures such as group testing and fractional replication can greatly reduce the workload. The former is especially efficient when the presence of a characteristic in samples is low. Fractional replication can greatly reduce the amount of experimentation when some of the parameters associated with a factorial are nonexistent or negligible. Supersaturated fractional replication can be used to efficiently screen factors when it is suspected that they may not affect a process but it is desired to check this suspicion. There are many types of grouping and pooling material in an investigation. Some of these are discussed as are the interrelationships among the above procedures.

Fractional replication in simulation studies

It is shown how to use fractional replication in simulation studies. Examples are given. Considerable savings in number of runs required can be achieved through the use of fractional replication ideas.

Nutrient-limitation effects on the biochemical composition of Cyclotella meneghiniana (Bacillariophyta): an experimental and statistical analysis

The lipid, fatty acid, glucan, protein, and chlorophyll contents of nutrient-starved and nutrient-stressed cells of Cyclotella meneghiniana Kütz. were investigated in batch and semicontinuous culture experiments, respectively. In batch culture experiments, cells were removed from nutrient-replete media, resuspended in silicon-, nitrogen-, or phosphorus-deficient media according to a 2 × 3 factorial design in fractional replication, and analyzed 3 and 9 days after transfer to treatment media. Silicon starvation caused a significant increase (300%) in cell protein content. In semicontinuous culture experiments, cells were grown in media with silicon, nitrogen, or phosphorus at concentrations lower than necessary for maximum rates of growth. Within each nutrient experiment, dilution rates of 0.10, 0.25, and 0.50∙day−1 produced three distinct rates of nutrient supply per cell. Cell lipid : glucan ratios significantly decreased (50%) with increasing silicon supply rate. Cell lipid, glucan, and protein significantly increased (300%) with increasing nitrogen supply rate. Cell lipid and glucan significantly increased (300 and 400%, respectively) with increasing phosphorus supply rate. Fatty acids of extracted lipids generally possessed carbon chain lengths of 14 to 24. However, carbon chain lengths of fatty acids from silicon-stressed cells ranged from less than 14 to 18. No distinct differences in fatty acid composition were observed among supply rates within silicon- and nitrogen-stressed cultures.

The Importance of Practice in the Development of Statistics

The article shows how application and consideration of the scientific context in which statistics is used can initiate important advances such as least squares, ratio estimators, correlation, contingency tables, studentization, experimental design, the analysis of variance, randomization, fractional replication, variance component analysis, bioassay, limits for a ratio, quality control, sampling inspection, nonparametric tests, transformation theory, ARIMA time series models, sequential tests, cumulative sum charts, data analysis plotting techniques, and a resolution of the Bayes-frequentist controversy. It appears that advances of this kind are frequently made because practical context reveals a novel formulation that eliminates an unnecessarily limiting framework.

The Importance of Practice in the Development of Statistics

The article shows how application and consideration of the scientific context in which statistics is used can initiate important advances such as least squares, ratio estimators, correlation, contingency tables, studentization, experimental design, the analysis of variance, randomization, fractional replication, variance component analysis, bioassay, limits for a ratio, quality control, sampling inspection, nonparametric tests, transformation theory, ARIMA time series models, sequential tests, cumulative sum charts, data analysis plotting techniques, and a resolution of the Bayes-frequentist controversy. It appears that advances of this kind are frequently made because practical context reveals a novel formulation that eliminates an unnecessarily limiting framework.

Further Results on Invariance and Randomization in Fractional Replication

The partitioning of the complete parametric vector from the experimenter's viewpoint for the general mixed factorial gives rise to the usual four exhaustive cases, (i), (ii), (iii), and (iv). Cases (i) and (iv) may be viewed as special cases of cases (ii) and (iii) respectively in connection with the problem of spectrum invariance under the group of level permutations and the problem of unbiased estimation under a uniform randomized design. Srivastava, Raktoe and Pesotan (1976) resolved these problems for case (ii) and this paper does the same for case (iii) so that the study is now complete.

Applications of Statistics to Industrial Experimentation

Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.

Applications of Statistics to Industrial Experimentation.

Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.

The Use of Vignettes in Survey Research

The use of vignettes—systematically elaborated descriptions of concrete situations–is supported as a means of producing more valid and more reliable measures of respondent opinion than the “simpler” abstract questions more typical of opinion surveys. The fractional replication experimental design described here enables a wide range of situation characteristics to be included and varied in the presentations made to various respondents while minimizing the number of different vignette versions required for the research instrument. Results from a study of police and nurse reactions to crime victims are shown as an example of this technique

On Invariance and Randomization in Fractional Replication

This paper generalizes the results of Paik and Federer (1970), Ehrenfeld and Zacks (1961) and Zacks (1963, 1964) regarding invariance and randomization in fractional replication. It is shown that (i) the characteristic roots of the information matrix of a design in the general factorial relative to an admissible vector of effects remain invariant under a permutation of levels; (ii) the unbiased estimation of a linear function of an admissible vector of effects can be obtained under equal probability randomization. In addition some applications of the results are indicated.

Analysis of Nonorthogonal $n$-Way Classifications

Four problems associated with the use of Zelen's calculus of factorials in the statistical analysis of nonorthogonal $n$-way classification data are solved. These are for the situations for which (i) some effect parameters are equated to zero, (ii) some combinations (subclasses) contain no observations, (iii) expected values of mean squares under fixed, mixed, and random models are desired, and (iv) expected values of single degree of freedom sums of squares are wanted. A unified approach to these problems was developed. Relationships to previous work, to blocked experiments, to fractional replication, and to "messy data" situations are discussed. The various analyses are first described for a nonorthogonal two-way classification and then generalized to an $n$-way classification in the final section of the paper. Numerical examples are presented to illustrate the various procedures.

Generalized Least-Squares Estimation of a Subvector of Parameters in Randomized Fractional Factorial Experiments

In fractional replication, the problem is to estimate a subvector, $\alpha$, of $S = p^s$ pre-assigned parameters in the presence of an additional subvector of nuisance parameters. Estimation procedures for randomized fractional replicates in $2^m$ factorial systems have been treated by Ehrenfeld and Zacks [1], [2] and Zacks [6], [7] under an orthogonalized form of the statistical model. Extension to systems with general prime $p$ has recently been studied under a "fully orthogonalized" model by Lentner [4]; this is discussed in Section 3. The generalized inverse operator is then applied to the study of estimation procedures in general $N = p^m$ fractional replication. The present work differs from that of Zacks [7] where the problem of estimating the entire vector of $N$ parameters was considered. The class of all type-$g$ (generalized inverse) solutions for $\alpha$ is given and the class is investigated with respect to unbiasedness and optimality. Specifically, it is shown that there is a unique unbiased type-$g$ estimator which coincides with the classical estimator under the assumption of zero nuisance parameters. Using the trace of the mean square error matrix as the risk function, it is shown that there is a coincidence of Bayes, minimax, admissible, and classical procedures under certain conditions.