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by Radia M. Johnson, Paul Gerrard
Mastering Scientific Computing with R
Mastering Scientific Computing with R
Table of Contents
Mastering Scientific Computing with R
Credits
About the Authors
About the Reviewers
www.PacktPub.com
Support files, eBooks, discount offers, and more
Why subscribe?
Free access for Packt account holders
Preface
What this book covers
What you need for this book
Who this book is for
Conventions
Reader feedback
Customer support
Downloading the example code
Downloading the color images of this book
Errata
Piracy
Questions
1. Programming with R
Data structures in R
Atomic vectors
Operations on vectors
Lists
Attributes
Factors
Multidimensional arrays
Matrices
Data frames
Loading data into R
Saving data frames
Basic plots and the ggplot2 package
Flow control
The for() loop
The apply() function
The if() statement
The while() loop
The repeat{} and break statement
Functions
General programming and debugging tools
Summary
2. Statistical Methods with R
Descriptive statistics
Data variability
Confidence intervals
Probability distributions
Fitting distributions
Higher order moments of a distribution
Other statistical tests to fit distributions
The propagate package
Hypothesis testing
Proportion tests
Two sample hypothesis tests
Unit root tests
Summary
3. Linear Models
An overview of statistical modeling
Model formulas
Explanatory variables interactions
Error terms
The intercept as parameter 1
Updating a model
Linear regression
Plotting a slope
Analysis of variance
Generalized linear models
Generalized additive models
Linear discriminant analysis
Principal component analysis
Clustering
Summary
4. Nonlinear Methods
Nonparametric and parametric models
The adsorption and body measures datasets
Theory-driven nonlinear regression
Visually exploring nonlinear relationships
Extending the linear framework
Polynomial regression
Performing a polynomial regression in R
Spline regression
Nonparametric nonlinear methods
Kernel regression
Kernel weighted local polynomial fitting
Optimal bandwidth selection
A practical scientific application of kernel regression
Locally weighted polynomial regression and the loess function
Nonparametric methods with the np package
Nonlinear quantile regression
Summary
5. Linear Algebra
Matrices and linear algebra
Matrices in R
Vectors in R
Matrix notation
The physical functioning dataset
Basic matrix operations
Element-wise matrix operations
Matrix subtraction
Matrix addition
Matrix sweep
Basic matrixwise operations
Transposition
Matrix multiplication
Multiplying square matrices for social networks
Outer products
Using sparse matrices in matrix multiplication
Matrix inversion
Solving systems of linear equations
Determinants
Triangular matrices
Matrix decomposition
QR decomposition
Eigenvalue decomposition
Lower upper decomposition
Cholesky decomposition
Singular value decomposition
Applications
Rasch analysis using linear algebra and a paired comparisons matrix
Calculating Cronbach's alpha
Image compression using direct cosine transform
Importing an image into R
The compression technique
Creating the transformation and quantization matrices
Putting the matrices together for image compression
DCT in R
Summary
6. Principal Component Analysis and the Common Factor Model
A primer on correlation and covariance structures
Datasets used in this chapter
Principal component analysis and total variance
Understanding the basics of PCA
How does PCA relate to SVD?
Scaled versus unscaled PCA
PCA for dimension reduction
PCA to summarize wine properties
Choosing the number of principal components to retain
Formative constructs using PCA
Exploratory factor analysis and reflective constructs
Familiarizing yourself with the basic terms
Matrices of interest
Expressing factor analysis in a matrix model
Basic EFA and concepts of covariance algebra
Concepts of EFA estimation
The centroid method
Multiple actors
Direct factor extraction by principal axis factoring
Performing principal axis factoring in R
Other factor extraction methods
Factor rotation
Orthogonal factor rotation methods
Quartimax rotation
Varimax rotation
Oblique rotations
Oblimin rotation
Promax rotation
Factor rotation in R
Advanced EFA with the psych package
Summary
7. Structural Equation Modeling and Confirmatory Factor Analysis
Datasets
Political democracy
Physical functioning dataset
Holzinger-Swineford 1939 dataset
The basic ideas of SEM
Components of an SEM model
Path diagram
Matrix representation of SEM
The reticular action model (RAM)
An example of SEM specification
An example in R
SEM model fitting and estimation methods
Assessing SEM model fit
Using OpenMx and matrix specification of an SEM
Summarizing the OpenMx approach
Explaining an entire example
Specifying the model matrices
Fitting the model
Fitting SEM models using lavaan
The lavaan syntax
Comparing OpenMx to lavaan
Explaining an example in lavaan
Explaining an example in OpenMx
Summary
8. Simulations
Basic sample simulations in R
Pseudorandom numbers
The runif() function
Bernoulli random variables
Binomial random variables
Poisson random variables
Exponential random variables
Monte Carlo simulations
Central limit theorem
Using the mc2d package
One-dimensional Monte Carlo simulation
Two-dimensional Monte Carlo simulation
Additional mc2d functions
The mcprobtree() function
The cornode() function
The mcmodel() function
The evalmcmod() function
Data visualization
Multivariate nodes
Monte Carlo integration
Multiple integration
Other density functions
Rejection sampling
Importance sampling
Simulating physical systems
Summary
9. Optimization
One-dimensional optimization
The golden section search method
The optimize() function
The Newton-Raphson method
The Nelder-Mead simplex method
More optim() features
Linear programming
Integer-restricted optimization
Unrestricted variables
Quadratic programming
General non-linear optimization
Other optimization packages
Summary
10. Advanced Data Management
Cleaning datasets in R
String processing and pattern matching
Regular expressions
Floating point operations and numerical data types
Memory management in R
Basic R memory commands
Handling R objects in memory
Missing data
Computational aspects of missing data in R
Statistical considerations of missing data
Deletion methods
Listwise deletion or complete case analysis
Pairwise deletion
Visualizing missing data
An overview of multiple imputation
Imputation basic principles
Approaches to imputation
The Amelia package
Getting estimates from multiply imputed datasets
Extracting the mean
Extracting the standard error of the mean
The mice package
Imputation functions in mice
Summary
Index
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Prev
Previous Chapter
Summary
Index
A
abline() function /
Plotting a slope
Adsorption
about /
Theory-driven nonlinear regression
adsorption dataset
about /
The adsorption and body measures datasets
URL /
The adsorption and body measures datasets
agrep function /
String processing and pattern matching
Akaike information criterion (AIC) value /
The propagate package
amelia command /
The Amelia package
Amelia package
about /
The Amelia package
estimates, obtaining from multiply imputed datasets /
Getting estimates from multiply imputed datasets
Analysis of variance (Anova)
about /
Analysis of variance
anova() function /
Analysis of variance
aov() function /
Analysis of variance
apply() function /
The apply() function
array() function /
Multidimensional arrays
atomic vectors
about /
Atomic vectors
operations /
Operations on vectors
attributes /
Attributes
Augmented Dickey-Fuller (ADF) /
Unit root tests
B
basic plots
creating /
Basic plots and the ggplot2 package
Bernoulli random variables /
Bernoulli random variables
binomial exact test /
Proportion tests
Binomial random variables /
Binomial random variables
biplot() function /
Principal component analysis
body measures dataset
about /
The adsorption and body measures datasets
bootstrap approach /
Hypothesis testing
boxplot command /
Nonparametric nonlinear methods
break statement /
The repeat{} and break statement
Brownian motion /
Simulating physical systems
browser() function /
General programming and debugging tools
Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm /
More optim() features
C
CDC
URL /
The physical functioning dataset
central limit theorem /
Central limit theorem
centroid method /
The centroid method
CERN's Root
URL /
Memory management in R
character classes, R
[aeiou] /
Regular expressions
[AEIOU] /
Regular expressions
[0-9] /
Regular expressions
[a-z] /
Regular expressions
[A-Z] /
Regular expressions
[a-zA-Z0-9] /
Regular expressions
[^0-9] /
Regular expressions
[[$alpha$]] /
Regular expressions
[[$punct$]] /
Regular expressions
[[$print$]] /
Regular expressions
[[$digit$]] /
Regular expressions
chartSeries() function /
Unit root tests
Chi-squared /
Two sample hypothesis tests
cholesky decomposition
about /
Cholesky decomposition
class() function /
Attributes
classical test theory (CTT)
about /
Calculating Cronbach's alpha
clustering
about /
Clustering
comma-separated values (CSV) file
URL /
The adsorption and body measures datasets
complete case analysis /
Listwise deletion or complete case analysis
Confidence intervals (CI) /
Confidence intervals
cornode() function /
The cornode() function
correlation matrices
about /
A primer on correlation and covariance structures
covariance matrices
about /
A primer on correlation and covariance structures
CRAN distributions page
URL /
Probability distributions
CRAN page
URL /
Using the mc2d package
CRAN R project Time Series Analysis website
URL /
Unit root tests
Cronbach's alpha
calculating /
Calculating Cronbach's alpha
D
data
loading, in R /
Loading data into R
data frames /
Data frames
saving /
Saving data frames
dataset /
The physical functioning dataset
about /
Datasets used in this chapter
red wine /
Datasets used in this chapter
abalone /
Datasets used in this chapter
physical functioning /
Datasets used in this chapter
datasets
about /
Datasets
political democracy /
Political democracy
physical functioning dataset /
Physical functioning dataset
Holzinger-Swineford 1939 dataset /
Holzinger-Swineford 1939 dataset
cleaning, in R /
Cleaning datasets in R
data structures, in R
about /
Data structures in R
homogeneous /
Data structures in R
heterogeneous /
Data structures in R
atomic vectors /
Atomic vectors
lists /
Lists
attributes /
Attributes
Factors /
Factors
multidimensional arrays /
Multidimensional arrays
data frames /
Data frames
data variability
about /
Data variability
Confidence intervals (CI) /
Confidence intervals
data visualization /
Data visualization
DCT
in R /
DCT in R
debugging tools
about /
General programming and debugging tools
deletion
using, as method /
Pairwise deletion
deletion methods
about /
Deletion methods
listwise deletion /
Listwise deletion or complete case analysis
complete case analysis /
Listwise deletion or complete case analysis
pairwise deletion /
Pairwise deletion
density functions /
Other density functions
descriptive statistics
about /
Descriptive statistics
data variability /
Data variability
diagonal matrix /
Matrix notation
dim() function /
Attributes
dimension reduction
PCA for /
PCA for dimension reduction
distributions
fitting, statistical tests used /
Other statistical tests to fit distributions
dnorm() function /
Probability distributions
E
EFA
about /
Exploratory factor analysis and reflective constructs
Latent trait or common factor /
Familiarizing yourself with the basic terms
Path coefficient /
Familiarizing yourself with the basic terms
Communality /
Familiarizing yourself with the basic terms
Uniqueness /
Familiarizing yourself with the basic terms
Observed /
Familiarizing yourself with the basic terms
Implied /
Familiarizing yourself with the basic terms
Orthogonal factor structure /
Familiarizing yourself with the basic terms
Oblique factor structure /
Familiarizing yourself with the basic terms
in matrix model /
Expressing factor analysis in a matrix model
covariance algebra /
Basic EFA and concepts of covariance algebra
estimation /
Concepts of EFA estimation
centroid method /
The centroid method
multiple actors /
Multiple actors
direct factor extraction, by principal axis factoring /
Direct factor extraction by principal axis factoring
principal axis factoring, performing in R /
Performing principal axis factoring in R
extraction methods /
Other factor extraction methods
factor rotation /
Factor rotation
advanced EFA, with psych package /
Advanced EFA with the psych package
effective degrees of freedom (edf) /
Generalized additive models
eigenvalue decomposition
about /
Eigenvalue decomposition
,
Lower upper decomposition
Element-wise matrix operations
about /
Element-wise matrix operations
matrix subtraction /
Matrix subtraction
matrix addition /
Matrix addition
matrix sweep /
Matrix sweep
error structure, canonical link functions
about /
Generalized linear models
estimates
obtaining, from multiply imputed datasets /
Getting estimates from multiply imputed datasets
evalmcmod() function /
The evalmcmod() function
example, in R /
An example in R
example, lavaan
defining /
Explaining an example in lavaan
example, OpenMx
defining /
Explaining an example in OpenMx
example, SEM specification /
An example of SEM specification
Exploratory factor analysis (EFA) /
The basic ideas of SEM
exponential random variables /
Exponential random variables
expression() function /
The propagate package
F
Factor correlation matrix /
Matrices of interest
Factor pattern matrix /
Matrices of interest
factor rotation
about /
Factor rotation
in R /
Factor rotation in R
factor rotation, methods
Quartimax rotation /
Quartimax rotation
Varimax rotation /
Varimax rotation
Oblique rotations /
Oblique rotations
Oblimin rotation /
Oblimin rotation
Promax rotation /
Promax rotation
Factors /
Factors
first mean value theorem /
Monte Carlo integration
Fisher's Exact test /
Two sample hypothesis tests
fitDistr() function /
The propagate package
fitMeasures command /
The lavaan syntax
fitting distributions
about /
Fitting distributions
higher order moments, of distribution /
Higher order moments of a distribution
statistical tests, for fitting distributions /
Other statistical tests to fit distributions
floating point operations
about /
Floating point operations and numerical data types
flow control
about /
Flow control
for() loop /
The for() loop
if() statement /
The if() statement
while() loop /
The while() loop
repeat{} statement /
The repeat{} and break statement
break statement /
The repeat{} and break statement
for() loop
about /
The for() loop
apply() function /
The apply() function
formative constructs
PCA used /
Formative constructs using PCA
functions
about /
Functions
used, for fitting distributions /
Other statistical tests to fit distributions
G
gam() function /
Generalized additive models
generalized additive models (GAMs)
about /
Generalized additive models
generalized linear model (GLM)
about /
Generalized linear models
general non-linear optimization
about /
General non-linear optimization
getwd() function /
Unit root tests
ggbiplot package
URL /
Principal component analysis
ggplot2 package
about /
Basic plots and the ggplot2 package
glm() function /
Generalized linear models
Golden section search method /
The golden section search method
grep function /
String processing and pattern matching
grepl function /
String processing and pattern matching
gridsize argument /
Kernel weighted local polynomial fitting
gsub function /
String processing and pattern matching
H
Holzinger-Swineford 1939 dataset /
Holzinger-Swineford 1939 dataset
hypothesis testing
about /
Hypothesis testing
proportion tests /
Proportion tests
two sample hypothesis tests /
Two sample hypothesis tests
unit root tests /
Unit root tests
I
identity matrix /
Matrix notation
if() statement /
The if() statement
image
importing, to R /
Importing an image into R
image compression
direct consine transform used /
Image compression using direct cosine transform
image, importing into R /
Importing an image into R
about /
The compression technique
matrices, putting together for /
Putting the matrices together for image compression
Implied correlation matrix /
Matrices of interest
importance sampling
about /
Importance sampling
imputation
approaches to /
Approaches to imputation
imputation functions, in MICE
about /
Imputation functions in mice
integer-restricted optimization /
Integer-restricted optimization
intercept, as parameter 1
about /
The intercept as parameter 1
model, updating /
Updating a model
item response theory (IRT)
about /
Calculating Cronbach's alpha
K
Kaiser Guttman rule /
Choosing the number of principal components to retain
kernel regression /
Kernel regression
scientific application /
A practical scientific application of kernel regression
kernel weighted local polynomial fitting
about /
Kernel weighted local polynomial fitting
optimal bandwidth selection /
Optimal bandwidth selection
scientific application, of kernel regression /
A practical scientific application of kernel regression
ksmooth function /
Kernel regression
Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test /
Unit root tests
L
Langmuir adsorption model
about /
Theory-driven nonlinear regression
lavaan
used, for fitting SEM models /
Fitting SEM models using lavaan
OpenMx, comparing to /
Comparing OpenMx to lavaan
example, defining /
Explaining an example in lavaan
lavaan command /
The lavaan syntax
lavaan syntax /
The lavaan syntax
lda() function /
Linear discriminant analysis
length() function /
Matrices
Levels /
Factors
linear algebra
used, for Rasch analysis /
Rasch analysis using linear algebra and a paired comparisons matrix
Linear discriminant analysis (LDA)
about /
Linear discriminant analysis
linear framework
extending /
Extending the linear framework
polynomial regression /
Polynomial regression
polynomial regression, performing in R /
Performing a polynomial regression in R
spline regression /
Spline regression
linear programming
about /
Linear programming
integer-restricted optimization /
Integer-restricted optimization
unrestricted variables /
Unrestricted variables
linear regression
about /
Linear regression
slope, plotting /
Plotting a slope
lists /
Lists
listwise deletion /
Listwise deletion or complete case analysis
locally weighted polynomial regression /
Locally weighted polynomial regression and the loess function
locpoly command /
Kernel weighted local polynomial fitting
loess command /
Locally weighted polynomial regression and the loess function
loess function /
Locally weighted polynomial regression and the loess function
lp() function /
Unrestricted variables
M
matrices /
Matrices
about /
Matrices and linear algebra
in R /
Matrices in R
rectangular /
Matrix notation
square /
Matrix notation
diagonal /
Matrix notation
triangular /
Matrix notation
symmetric /
Matrix notation
identity /
Matrix notation
vector /
Matrix notation
sparse matrix /
Matrix notation
A /
The reticular action model (RAM)
S /
The reticular action model (RAM)
F /
The reticular action model (RAM)
matrix
about /
Matrices and linear algebra
subtraction /
Matrix subtraction
addition /
Matrix addition
sweep /
Matrix sweep
multiplication /
Matrix multiplication
Reduced correlation matrix /
Matrices of interest
Implied correlation matrix /
Matrices of interest
Residual correlation matrix /
Matrices of interest
Factor pattern matrix /
Matrices of interest
Factor correlation matrix /
Matrices of interest
Uniqueness matrix /
Matrices of interest
matrix-wise operations, basic
about /
Basic matrixwise operations
transposition /
Transposition
matrix multiplication /
Matrix multiplication
matrix inversion /
Matrix inversion
determinants /
Determinants
matrix decomposition
about /
Matrix decomposition
QR decomposition /
QR decomposition
eigenvalue decomposition /
Eigenvalue decomposition
lower upper decomposition /
Lower upper decomposition
cholesky decomposition /
Cholesky decomposition
singular value decomposition /
Singular value decomposition
matrix inversion
about /
Matrix inversion
linear equations, systems solving /
Solving systems of linear equations
matrix multiplication
about /
Matrix multiplication
square matrices, multiplying for social networks /
Multiplying square matrices for social networks
outer products /
Outer products
sparse matrices using /
Using sparse matrices in matrix multiplication
matrix operations
about /
Basic matrix operations
element-wise matrix operations /
Element-wise matrix operations
matrix-wise operations /
Basic matrixwise operations
matrix representation, SEM
about /
Matrix representation of SEM
reticular action model (REM) /
The reticular action model (RAM)
example, in R /
An example in R
matrix specification
using /
Using OpenMx and matrix specification of an SEM
mc2d documentation
URL /
Additional mc2d functions
mc2d functions
about /
Additional mc2d functions
mcprobtree() function /
The mcprobtree() function
cornode() function /
The cornode() function
mcmodel() function /
The mcmodel() function
evalmcmod() function /
The evalmcmod() function
data visualization /
Data visualization
mc2d package
using /
Using the mc2d package
one-dimensional Monte Carlo simulation /
One-dimensional Monte Carlo simulation
two-dimensional Monte Carlo simulation /
Two-dimensional Monte Carlo simulation
mc2d functions /
Additional mc2d functions
multivariate nodes /
Multivariate nodes
mcmodel() function /
The mcmodel() function
mcprobtree() function /
The mcprobtree() function
mean
extracting /
Extracting the mean
mean() function /
Data variability
Mean Value theorem /
Monte Carlo integration
memory
R objects, handling in /
Handling R objects in memory
memory management, in R
about /
Memory management in R
R memory commands /
Basic R memory commands
R objects, handling in memory /
Handling R objects in memory
mice command /
Imputation functions in mice
MICE package
about /
The mice package
imputation functions /
Imputation functions in mice
missing data
about /
Missing data
computational aspects, in R /
Computational aspects of missing data in R
statistical considerations /
Statistical considerations of missing data
dealing with /
Statistical considerations of missing data
deletion methods /
Deletion methods
visualizing /
Visualizing missing data
multiple imputation /
An overview of multiple imputation
model
updating /
Updating a model
fitting /
Fitting the model
model formulas, statistical modeling /
Model formulas
model matrices
specifying /
Specifying the model matrices
model, fitting /
Fitting the model
Monte Carlo integration
about /
Monte Carlo integration
multiple integration /
Multiple integration
density functions /
Other density functions
Monte Carlo simulations
about /
Monte Carlo simulations
central limit theorem /
Central limit theorem
mc2d package, using /
Using the mc2d package
URL /
Using the mc2d package
multidimensional arrays
about /
Multidimensional arrays
matrices /
Matrices
multiple error terms, statistical modeling /
Error terms
multiple imputation
about /
An overview of multiple imputation
principle /
Imputation basic principles
multiple integration /
Multiple integration
multiply imputed datasets
estimates, obtaining from /
Getting estimates from multiply imputed datasets
mean, extracting /
Extracting the mean
standard error of mean, extracting /
Extracting the standard error of the mean
multivariate nodes /
Multivariate nodes
N
names() function /
Attributes
National Health and Nutrition Examination Survey (NHANES) /
The physical functioning dataset
,
Physical functioning dataset
Nelder-Mead simplex method /
The Nelder-Mead simplex method
URL /
The Nelder-Mead simplex method
Newton-Raphson method /
The Newton-Raphson method
nls command /
Theory-driven nonlinear regression
nonconvergence
problems /
Performing a polynomial regression in R
nonlinear quantile regression /
Nonlinear quantile regression
nonlinear relationships
exploring, visually /
Visually exploring nonlinear relationships
nonparametric methods, with np package
about /
Nonparametric methods with the np package
nonlinear quantile regression /
Nonlinear quantile regression
nonparametric model
about /
Nonparametric and parametric models
nonparametric nonlinear methods
about /
Nonparametric nonlinear methods
kernel regression /
Kernel regression
kernel weighted local polynomial fitting /
Kernel weighted local polynomial fitting
locally weighted polynomial regression /
Locally weighted polynomial regression and the loess function
loess function /
Locally weighted polynomial regression and the loess function
npqreg command /
Nonlinear quantile regression
numerical data types
about /
Floating point operations and numerical data types
O
Oblimin rotation /
Oblimin rotation
Oblique rotations /
Oblique rotations
one-dimensional Monte Carlo simulation /
One-dimensional Monte Carlo simulation
one-dimensional optimization
about /
One-dimensional optimization
Golden section search method /
The golden section search method
optimize() function /
The optimize() function
Newton-Raphson method /
The Newton-Raphson method
Nelder-Mead simplex method /
The Nelder-Mead simplex method
optim() function /
More optim() features
OpenMx
using /
Using OpenMx and matrix specification of an SEM
defining /
Summarizing the OpenMx approach
comparing, to lavaan /
Comparing OpenMx to lavaan
example, defining /
Explaining an example in OpenMx
optim() function /
More optim() features
optimal bandwidth selection /
Optimal bandwidth selection
optimization packages
about /
Other optimization packages
URL /
Other optimization packages
optimize() function /
The optimize() function
overimpute command /
The Amelia package
P
pairwise deletion /
Pairwise deletion
parametric model
about /
Nonparametric and parametric models
parametric regression models
advantages /
Nonparametric and parametric models
disadvantages /
Nonparametric and parametric models
paste() function /
Probability distributions
path diagram
about /
Path diagram
observed variable /
Path diagram
latent variable /
Path diagram
causal path /
Path diagram
residual /
Path diagram
correlation /
Path diagram
pattern matching
about /
String processing and pattern matching
PCA
about /
Principal component analysis and total variance
basics /
Understanding the basics of PCA
relating, to SVD /
How does PCA relate to SVD?
scaled versus unscaled PCA /
Scaled versus unscaled PCA
for dimension reduction /
PCA for dimension reduction
for summarizing wine properties /
PCA to summarize wine properties
number of principal components to retain, selecting /
Choosing the number of principal components to retain
used, for formative constructs /
Formative constructs using PCA
physical functioning dataset /
Physical functioning dataset
physical systems
simulating /
Simulating physical systems
plot() function /
Probability distributions
,
Unit root tests
,
Linear programming
plot3d() function
about /
Principal component analysis
Poisson random variables /
Poisson random variables
political democracy /
Political democracy
polynomial regression
about /
Polynomial regression
performing, in R /
Performing a polynomial regression in R
prcomp
and princomp /
Understanding the basics of PCA
prcomp() function /
Principal component analysis
predict() function /
Linear discriminant analysis
predict command /
Locally weighted polynomial regression and the loess function
principal axis factoring (PAF)
about /
Direct factor extraction by principal axis factoring
in R /
Performing principal axis factoring in R
principal component
about /
Understanding the basics of PCA
to retain, selecting /
Choosing the number of principal components to retain
Principal component analysis (PCA)
about /
Principal component analysis
princomp
and prcomp /
Understanding the basics of PCA
print() function /
Two-dimensional Monte Carlo simulation
probability distributions
about /
Probability distributions
programming tools
about /
General programming and debugging tools
Promax rotation /
Promax rotation
prop.test() function /
Two sample hypothesis tests
propagate() function /
The propagate package
propagate package /
The propagate package
proportion tests /
Proportion tests
pseudorandom numbers
about /
Pseudorandom numbers
runif() function /
The runif() function
Bernoulli random variables /
Bernoulli random variables
Binomial random variables /
Binomial random variables
Poisson random variables /
Poisson random variables
exponential random variables /
Exponential random variables
Q
qnorm() /
Probability distributions
QR decomposition
about /
QR decomposition
qt() function /
Confidence intervals
quadratic programming
about /
Quadratic programming
Quantile-Quantile plot (Q-Q plot) /
Fitting distributions
quantization matrix
creating /
Creating the transformation and quantization matrices
Quartimax rotation /
Quartimax rotation
R
R
data, loading into /
Loading data into R
polynomial regression, performing in /
Performing a polynomial regression in R
matrices /
Matrices in R
vectors /
Vectors in R
image, importing into /
Importing an image into R
DCT /
DCT in R
datasets, cleaning in /
Cleaning datasets in R
computational aspects, of missing data /
Computational aspects of missing data in R
Rasch analysis
linear algebra used /
Rasch analysis using linear algebra and a paired comparisons matrix
rbern() function /
Bernoulli random variables
rectangular matrix /
Matrix notation
Reduced correlation matrix /
Matrices of interest
Regular Expressions
about /
String processing and pattern matching
regular expressions
about /
Regular expressions
. /
Regular expressions
$ /
Regular expressions
? /
Regular expressions
* /
Regular expressions
+ /
Regular expressions
^ /
Regular expressions
| /
Regular expressions
[ ] /
Regular expressions
{ } /
Regular expressions
\d /
Regular expressions
\D /
Regular expressions
\s /
Regular expressions
\S /
Regular expressions
\w /
Regular expressions
\W /
Regular expressions
rejection sampling
about /
Rejection sampling
rep() function /
Atomic vectors
repeat{} statement /
The repeat{} and break statement
require() function /
Loading data into R
Residual correlation matrix /
Matrices of interest
result argument /
The cornode() function
Reticular action model (RAM) /
Matrix representation of SEM
reticular action model (REM)
about /
The reticular action model (RAM)
example, SEM specification /
An example of SEM specification
R memory commands /
Basic R memory commands
rnom() function /
The propagate package
rnorm() function /
Two-dimensional Monte Carlo simulation
R objects
handling, in memory /
Handling R objects in memory
Root Mean Square Error of Approximation (RMSEA) /
Advanced EFA with the psych package
Root Mean Square Residual (RMSR) /
Advanced EFA with the psych package
round() function /
Descriptive statistics
rpois() /
Probability distributions
runif() function /
The runif() function
S
sample() function /
Basic sample simulations in R
sapply command /
Extracting the mean
scaled PCA
versus unscaled PCA /
Scaled versus unscaled PCA
scatter.smooth command /
Visually exploring nonlinear relationships
Screen test /
Choosing the number of principal components to retain
SEM
about /
The basic ideas of SEM
SEM model
components /
Components of an SEM model
observed variable /
Components of an SEM model
latent variable /
Components of an SEM model
path /
Components of an SEM model
residual /
Components of an SEM model
covariance algebra /
Components of an SEM model
path diagram /
Path diagram
fitting /
SEM model fitting and estimation methods
estimation methods /
SEM model fitting and estimation methods
fit, assessing /
Assessing SEM model fit
OpenMx, using /
Using OpenMx and matrix specification of an SEM
matrix specification, using /
Using OpenMx and matrix specification of an SEM
OpenMx, defining /
Summarizing the OpenMx approach
example /
Explaining an entire example
model matrices, specifying /
Specifying the model matrices
fitting, lavaan used /
Fitting SEM models using lavaan
lavaan syntax /
The lavaan syntax
SEM model fit
assessing /
Assessing SEM model fit
indices /
Assessing SEM model fit
seq() function /
Atomic vectors
setwd() function /
Unit root tests
simulations, R
about /
Basic sample simulations in R
single imputation /
Imputation basic principles
singular value decomposition
about /
Singular value decomposition
skewness() function /
Higher order moments of a distribution
slope, linear regression
plotting /
Plotting a slope
solnp() function /
General non-linear optimization
sparse matrices
using, in matrix multiplication /
Using sparse matrices in matrix multiplication
sparse matrix /
Matrix notation
Spectral Tests
URL /
Pseudorandom numbers
spline regression /
Spline regression
sqrt() function /
Data variability
square matrix /
Matrix notation
standard deviation /
Data variability
standard error, of mean
extracting /
Extracting the standard error of the mean
statistical considerations, missing data
about /
Statistical considerations of missing data
missing completely at random (MCAR) /
Statistical considerations of missing data
missing at random (MAR) /
Statistical considerations of missing data
missing not at random (MNAR) /
Statistical considerations of missing data
statistical modeling
about /
An overview of statistical modeling
model formulas /
Model formulas
variables, interaction between /
Explanatory variables interactions
multiple error terms /
Error terms
intercept, as parameter 1 /
The intercept as parameter 1
statistical tests
used, for fitting distributions /
Other statistical tests to fit distributions
propagate package /
The propagate package
str() function /
Atomic vectors
string processing
about /
String processing and pattern matching
sub function /
String processing and pattern matching
sum() function /
Data variability
summary() function /
Descriptive statistics
summary command /
Theory-driven nonlinear regression
SVD
PCA, relating to /
How does PCA relate to SVD?
symbols, statistical modeling
- /
Model formulas
* /
Model formulas
/ /
Model formulas
| /
Model formulas
$ /
Model formulas
I /
Model formulas
symmetric matrix /
Matrix notation
system.time command /
Handling R objects in memory
T
theory-driven nonlinear regression
about /
Theory-driven nonlinear regression
tilde (~) symbol
about /
Model formulas
transformation matrix
creating /
Creating the transformation and quantization matrices
about /
Creating the transformation and quantization matrices
tri.mat function /
Triangular matrices
triangular matrices /
Triangular matrices
triangular matrix /
Matrix notation
ts() function /
Unit root tests
Tucker-Lewis Index (TLI) /
Advanced EFA with the psych package
two-dimensional Monte Carlo simulation /
Two-dimensional Monte Carlo simulation
two sample hypothesis tests /
Two sample hypothesis tests
U
UCI Machine Learning Repository /
Datasets used in this chapter
UC Irvine Machine Learning Repository dataset /
Datasets used in this chapter
Uniqueness matrix /
Matrices of interest
unit root tests /
Unit root tests
unrestricted variables /
Unrestricted variables
unscaled PCA
versus scaled PCA /
Scaled versus unscaled PCA
V
variables
interactions between /
Explanatory variables interactions
Varimax rotation /
Varimax rotation
vector matrix /
Matrix notation
vectors
about /
Matrices and linear algebra
in R /
Vectors in R
W
while() loop /
The while() loop
wilcox.test() function /
Hypothesis testing
Wilcoxon signed-rank test /
Hypothesis testing
with.imputationList command /
Extracting the standard error of the mean
with command /
Imputation functions in mice
Z
Z-test /
Proportion tests
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