One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. We have implemented the Satterthwaite's method for approximating degrees of freedom for the t and F tests. We have also implemented the construction of Type I - III ANOVA tables. Furthermore, one may also obtain the summary as well as the anova table using the Kenward-Roger approximation for denominator degrees of freedom (based on the KRmodcomp function from the pbkrtest package). Some other convenient mixed model analysis tools such as a step method, that performs backward elimination of nonsignificant effects - both random and fixed, calculation of population means and multiple comparison tests together with plot facilities are provided by the package as well.

/pdf/lmertest-package-tests-in-linear-mixed-effects-models-1x6b86x8v9.pdf

lmerTest Package: Tests in Linear Mixed Effects Models

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Modern Applied Statistics With S

In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

Extended-connectivity fingerprints (ECFPs) are a novel class of topological fingerprints for molecular characterization. Historically, topological fingerprints were developed for substructure and similarity searching. ECFPs were developed specifically for structure−activity modeling. ECFPs are circular fingerprints with a number of useful qualities: they can be very rapidly calculated; they are not predefined and can represent an essentially infinite number of different molecular features (including stereochemical information); their features represent the presence of particular substructures, allowing easier interpretation of analysis results; and the ECFP algorithm can be tailored to generate different types of circular fingerprints, optimized for different uses. While the use of ECFPs has been widely adopted and validated, a description of their implementation has not previously been presented in the literature.

Extended-Connectivity Fingerprints

The measurement of meaning

lmerTest: Tests for random and fixed effects for linear mixed effect models (lmer objects of lme4 package)

Tests in Linear Mixed Effects Models

Preface. Acknowledgements. 1 Introduction. 1.1 The Distinction between Trained Sensory Panels and Consumer Panels. 1.2 The Need for Statistics in Experimental Planning and Analysis. 1.3 Scales and Data Types. 1.4 Organisation of the Book. 2 Important Data Collection Techniques for Sensory and Consumer Studies. 2.1 Sensory Panel Methodologies. 2.2 Consumer Tests. PART I PROBLEM DRIVEN. 3 Quality Control of Sensory Profile Data. 3.1 General Introduction. 3.2 Visual Inspection of Raw Data. 3.3 Mixed Model ANOVA for Assessing the Importance of the Sensory Attributes. 3.4 Overall Assessment of Assessor Differences Using All Variables Simultaneously. 3.5 Methods for Detecting Differences in Use of the Scale. 3.6 Comparing the Assessors Ability to Detect Differences between the Products. 3.7 Relations between Individual Assessor Ratings and the Panel Average. 3.8 Individual Line Plots for Detailed Inspection of Assessors. 3.9 Miscellaneous Methods.- 4 Correction Methods and Other Remedies for Improving Sensory Profile Data. 4.1 Introduction. 4.2 Correcting for Different Use of the Scale. 4.3 Computing Improved Panel Averages. 4.4 Pre-processing of Data for Three-Way Analysis. 5 Detecting and Studying Sensory Differences and Similarities between Products. 5.1 Introduction. 5.2 Analysing Sensory Profile Data: Univariate Case. 5.3 Analysing Sensory Profile Data: Multivariate Case. 6 Relating Sensory Data to Other Measurements. 6.1 Introduction. 6.2 Estimating Relations between Consensus Profiles and External Data. 6.3 Estimating Relations between Individual Sensory Profiles and External Data. 7 Discrimination and Similarity Testing. 7.1 Introduction. 7.2 Analysis of Data from Basic Sensory Discrimination Tests. 7.3 Examples of Basic Discrimination Testing. 7.4 Power Calculations in Discrimination Tests. 7.5 Thurstonian Modelling: What Is It Really? 7.6 Similarity versus Difference Testing. 7.7 Replications: What to Do? 7.8 Designed Experiments, Extended Analysis and Other Test Protocols. 8 Investigating Important Factors Influencing Food Acceptance and Choice. 8.1 Introduction. 8.2 Preliminary Analysis of Consumer Data Sets (Raw Data Overview). 8.3 Experimental Designs for Rating Based Consumer Studies. 8.4 Analysis of Categorical Effect Variables. 8.5 Incorporating Additional Information about Consumers. 8.6 Modelling of Factors as Continuous Variables. 8.7 Reliability/Validity Testing for Rating Based Methods. 8.8 Rank Based Methodology. 8.9 Choice Based Conjoint Analysis. 8.10 Market Share Simulation. 9 Preference Mapping for Understanding Relations between Sensory Product Attributes and Consumer Acceptance. 9.1 Introduction. 9.2 External and Internal Preference Mapping. 9.3 Examples of Linear Preference Mapping. 9.4 Ideal Point Preference Mapping. 9.5 Selecting Samples for Preference Mapping. 9.6 Incorporating Additional Consumer Attributes. 9.7 Combining Preference Mapping with Additional Information about the Samples. 10 Segmentation of Consumer Data. 10.1 Introduction. 10.2 Segmentation of Rating Data. 10.3 Relating Segments to Consumer Attributes. PART II METHOD ORIENTED. 11 Basic Statistics. 11.1 Basic Concepts and Principles. 11.2 Histogram, Frequency and Probability. 11.3 Some Basic Properties of a Distribution (Mean, Variance and Standard Deviation). 11.4 Hypothesis Testing and Confidence Intervals for the Mean . 11.5 Statistical Process Control. 11.6 Relationships between Two or More Variables. 11.7 Simple Linear Regression. 11.8 Binomial Distribution and Tests. 11.9 Contingency Tables and Homogeneity Testing. 12 Design of Experiments for Sensory and Consumer Data. 12.1 Introduction. 12.2 Important Concepts and Distinctions. 12.3 Full Factorial Designs. 12.4 Fractional Factorial Designs: Screening Designs. 12.5 Randomised Blocks and Incomplete Block Designs. 12.6 Split-Plot and Nested Designs. 12.7 Power of Experiments. 13 ANOVA for Sensory and Consumer Data. 13.1 Introduction. 13.2 One-Way ANOVA. 13.3 Single Replicate Two-Way ANOVA. 13.4 Two-Way ANOVA with Randomised Replications. 13.5 Multi-Way ANOVA. 13.6 ANOVA for Fractional Factorial Designs. 13.7 Fixed and Random Effects in ANOVA: Mixed Models. 13.8 Nested and Split-Plot Models. 13.9 Post Hoc Testing. 14 Principal Component Analysis. 14.1 Interpretation of Complex Data Sets by PCA. 14.2 Data Structures for the PCA. 14.3 PCA: Description of the Method. 14.4 Projections and Linear Combinations. 14.5 The Scores and Loadings Plots. 14.6 Correlation Loadings Plot. 14.7 Standardisation. 14.8 Calculations and Missing Values. 14.9 Validation. 14.10 Outlier Diagnostics. 14.11 Tucker-1. 14.12 The Relation between PCA and Factor Analysis (FA). 15 Multiple Regression, Principal Components Regression and Partial Least Squares Regression. 15.1 Introduction. 15.2 Multivariate Linear Regression. 15.3 The Relation between ANOVA and Regression Analysis. 15.4 Linear Regression Used for Estimating Polynomial Models. 15.5 Combining Continuous and Categorical Variables. 15.6 Variable Selection for Multiple Linear Regression. 15.7 Principal Components Regression (PCR). 15.8 Partial Least Squares (PLS) Regression. 15.9 Model Validation: Prediction Performance. 15.10 Model Diagnostics and Outlier Detection. 15.11 Discriminant Analysis. 15.12 Generalised Linear Models, Logistic Regression and Multinomial Regression. 16 Cluster Analysis: Unsupervised Classification. 16.1 Introduction. 16.2 Hierarchical Clustering. 16.3 Partitioning Methods. 16.4 Cluster Analysis for Matrices. 17 Miscellaneous Methodologies. 17.1 Three-Way Analysis of Sensory Data. 17.2 Relating Three-Way Data to Two-Way Data. 17.3 Path Modelling. 17.4 MDS-Multidimensional Scaling. 17.5 Analysing Rank Data. 17.6 The L-PLS Method. 17.7 Missing Value Estimation. Nomenclature, Symbols and Abbreviations. Index.

Per B. Brockhoff

Papers

lmerTest Package: Tests in Linear Mixed Effects Models

lmerTest: Tests for random and fixed effects for linear mixed effect models (lmer objects of lme4 package)

Tests in Linear Mixed Effects Models

Statistics for Sensory and Consumer Science

Rapid descriptive sensory methods – Comparison of Free Multiple Sorting, Partial Napping, Napping, Flash Profiling and conventional profiling