Package 'logisticPCA' reference manual

Title:	Binary Dimensionality Reduction
Description:	Dimensionality reduction techniques for binary data including logistic PCA.
Authors:	Andrew J. Landgraf
Maintainer:	Andrew J. Landgraf <[email protected]>
License:	MIT + file LICENSE
Version:	0.2.9000
Built:	2024-09-07 04:05:23 UTC
Source:	https://github.com/andland/logisticpca

logisticPCA-package

Description

Dimension reduction techniques for binary data including logistic PCA

Author(s)

Andrew J. Landgraf

Convex Logistic Principal Component Analysis

Description

Dimensionality reduction for binary data by extending Pearson's PCA formulation to minimize Binomial deviance. The convex relaxation to projection matrices, the Fantope, is used.

Usage

convexLogisticPCA(
  x,
  k = 2,
  m = 4,
  quiet = TRUE,
  partial_decomp = FALSE,
  max_iters = 1000,
  conv_criteria = 1e-06,
  random_start = FALSE,
  start_H,
  mu,
  main_effects = TRUE,
  ss_factor = 4,
  weights,
  M
)
convexLogisticPCA(
  x,
  k = 2,
  m = 4,
  quiet = TRUE,
  partial_decomp = FALSE,
  max_iters = 1000,
  conv_criteria = 1e-06,
  random_start = FALSE,
  start_H,
  mu,
  main_effects = TRUE,
  ss_factor = 4,
  weights,
  M
)

Arguments

`x`	matrix with all binary entries
`k`	number of principal components to return
`m`	value to approximate the saturated model
`quiet`	logical; whether the calculation should give feedback
`partial_decomp`	logical; if `TRUE`, the function uses the RSpectra package to quickly initialize `H` and project onto the Fantope when `ncol(x)` is large and `k` is small
`max_iters`	number of maximum iterations
`conv_criteria`	convergence criteria. The difference between average deviance in successive iterations
`random_start`	logical; whether to randomly inititalize the parameters. If `FALSE`, function will use an eigen-decomposition as starting value
`start_H`	starting value for the Fantope matrix
`mu`	main effects vector. Only used if `main_effects = TRUE`
`main_effects`	logical; whether to include main effects in the model
`ss_factor`	step size multiplier. Amount by which to multiply the step size. Quadratic convergence rate can be proven for `ss_factor = 1`, but I have found higher values sometimes work better. The default is `ss_factor = 4`. If it is not converging, try `ss_factor = 1`.
`weights`	an optional matrix of the same size as the `x` with non-negative weights
`M`	depricated. Use `m` instead

Value

An S3 object of class clpca which is a list with the following components:

`mu`	the main effects
`H`	a rank `k` Fantope matrix
`U`	a `ceiling(k)`-dimentional orthonormal matrix with the loadings
`PCs`	the princial component scores
`m`	the parameter inputed
`iters`	number of iterations required for convergence
`loss_trace`	the trace of the average negative log likelihood using the Fantope matrix
`proj_loss_trace`	the trace of the average negative log likelihood using the projection matrix
`prop_deviance_expl`	the proportion of deviance explained by this model. If `main_effects = TRUE`, the null model is just the main effects, otherwise the null model estimates 0 for all natural parameters.
`rank`	the rank of the Fantope matrix `H`

References

Landgraf, A.J. & Lee, Y., 2020. Dimensionality reduction for binary data through the projection of natural parameters. Journal of Multivariate Analysis, 180, p.104668. https://arxiv.org/abs/1510.06112 https://doi.org/10.1016/j.jmva.2020.104668

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run convex logistic PCA on it
clpca = convexLogisticPCA(mat, k = 1, m = 4)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run convex logistic PCA on it
clpca = convexLogisticPCA(mat, k = 1, m = 4)

CV for convex logistic PCA

Description

Run cross validation on dimension and m for convex logistic PCA

Usage

cv.clpca(x, ks, ms = seq(2, 10, by = 2), folds = 5, quiet = TRUE, Ms, ...)
cv.clpca(x, ks, ms = seq(2, 10, by = 2), folds = 5, quiet = TRUE, Ms, ...)

Arguments

`x`	matrix with all binary entries
`ks`	the different dimensions `k` to try
`ms`	the different approximations to the saturated model `m` to try
`folds`	if `folds` is a scalar, then it is the number of folds. If it is a vector, it should be the same length as the number of rows in `x`
`quiet`	logical; whether the function should display progress
`Ms`	depricated. Use `ms` instead
`...`	Additional arguments passed to convexLogisticPCA

Value

A matrix of the CV negative log likelihood with k in rows and m in columns

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.clpca(mat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.clpca(mat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)

CV for logistic PCA

Description

Run cross validation on dimension and m for logistic PCA

Usage

cv.lpca(x, ks, ms = seq(2, 10, by = 2), folds = 5, quiet = TRUE, Ms, ...)
cv.lpca(x, ks, ms = seq(2, 10, by = 2), folds = 5, quiet = TRUE, Ms, ...)

Arguments

`x`	matrix with all binary entries
`ks`	the different dimensions `k` to try
`ms`	the different approximations to the saturated model `m` to try
`folds`	if `folds` is a scalar, then it is the number of folds. If it is a vector, it should be the same length as the number of rows in `x`
`quiet`	logical; whether the function should display progress
`Ms`	depricated. Use `ms` instead
`...`	Additional arguments passed to `logisticPCA`

Value

A matrix of the CV negative log likelihood with k in rows and m in columns

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lpca(mat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lpca(mat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)

CV for logistic SVD

Description

Run cross validation on dimension for logistic SVD

Usage

cv.lsvd(x, ks, folds = 5, quiet = TRUE, ...)
cv.lsvd(x, ks, folds = 5, quiet = TRUE, ...)

Arguments

`x`	matrix with all binary entries
`ks`	the different dimensions `k` to try
`folds`	if `folds` is a scalar, then it is the number of folds. If it is a vector, it should be the same length as the number of rows in `x`
`quiet`	logical; whether the function should display progress
`...`	Additional arguments passed to logisticSVD

Value

A matrix of the CV negative log likelihood with k in rows

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lsvd(mat, ks = 1:9)
plot(negloglikes)

## End(Not run)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lsvd(mat, ks = 1:9)
plot(negloglikes)

## End(Not run)

Fitted values using logistic PCA

Description

Fit a lower dimentional representation of the binary matrix using logistic PCA

Usage

## S3 method for class 'lpca'
fitted(object, type = c("link", "response"), ...)
## S3 method for class 'lpca'
fitted(object, type = c("link", "response"), ...)

Arguments

`object`	logistic PCA object
`type`	the type of fitting required. `type = "link"` gives output on the logit scale and `type = "response"` gives output on the probability scale
`...`	Additional arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

# construct fitted probability matrix
fit = fitted(lpca, type = "response")
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

# construct fitted probability matrix
fit = fitted(lpca, type = "response")

Fitted values using logistic SVD

Description

Fit a lower dimentional representation of the binary matrix using logistic SVD

Usage

## S3 method for class 'lsvd'
fitted(object, type = c("link", "response"), ...)
## S3 method for class 'lsvd'
fitted(object, type = c("link", "response"), ...)

Arguments

`object`	logistic SVD object
`type`	the type of fitting required. `type = "link"` gives output on the logit scale and `type = "response"` gives output on the probability scale
`...`	Additional arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

# construct fitted probability matrix
fit = fitted(lsvd, type = "response")
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

# construct fitted probability matrix
fit = fitted(lsvd, type = "response")

United States Congressional Voting Records 1984

Description

This data set includes votes for each of the U.S. House of Representatives Congressmen on the 16 key votes identified by the CQA. The CQA lists nine different types of votes: voted for, paired for, and announced for (these three simplified to yea), voted against, paired against, and announced against (these three simplified to nay), voted present, voted present to avoid conflict of interest, and did not vote or otherwise make a position known (these three simplified to an unknown disposition).

Usage

house_votes84
house_votes84

Format

A matrix with all binary or missing entries. There are 435 rows corresponding members of congress and 16 columns representing the bills being voted on. The row names refer to the political party of the members of congress

Source

Congressional Quarterly Almanac, 98th Congress, 2nd session 1984, Volume XL: Congressional Quarterly Inc., Washington, D.C., 1985

Data converted to a matrix from:

Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

Examples

data(house_votes84)
congress_lpca = logisticPCA(house_votes84, k = 2, m = 4)
data(house_votes84)
congress_lpca = logisticPCA(house_votes84, k = 2, m = 4)

Inverse logit for matrices

Description

Apply the inverse logit function to a matrix, element-wise. It generalizes the inv.logit function from the gtools library to matrices

Usage

inv.logit.mat(x, min = 0, max = 1)
inv.logit.mat(x, min = 0, max = 1)

Arguments

`x`	matrix
`min`	Lower end of logit interval
`max`	Upper end of logit interval

Examples

(mat = matrix(rnorm(10 * 5), nrow = 10, ncol = 5))
inv.logit.mat(mat)
(mat = matrix(rnorm(10 * 5), nrow = 10, ncol = 5))
inv.logit.mat(mat)

Bernoulli Log Likelihood

Description

Calculate the Bernoulli log likelihood of matrix

Usage

log_like_Bernoulli(x, theta, q)
log_like_Bernoulli(x, theta, q)

Arguments

`x`	matrix with all binary entries
`theta`	estimated natural parameters with same dimensions as x
`q`	instead of x, you can input matrix q which is -1 if `x = 0`, 1 if `x = 1`, and 0 if `is.na(x)`

Logistic Principal Component Analysis

Description

Dimensionality reduction for binary data by extending Pearson's PCA formulation to minimize Binomial deviance

Usage

logisticPCA(
  x,
  k = 2,
  m = 4,
  quiet = TRUE,
  partial_decomp = FALSE,
  max_iters = 1000,
  conv_criteria = 1e-05,
  random_start = FALSE,
  start_U,
  start_mu,
  main_effects = TRUE,
  validation,
  M,
  use_irlba
)
logisticPCA(
  x,
  k = 2,
  m = 4,
  quiet = TRUE,
  partial_decomp = FALSE,
  max_iters = 1000,
  conv_criteria = 1e-05,
  random_start = FALSE,
  start_U,
  start_mu,
  main_effects = TRUE,
  validation,
  M,
  use_irlba
)

Arguments

`x`	matrix with all binary entries
`k`	number of principal components to return
`m`	value to approximate the saturated model. If `m = 0`, m is solved for
`quiet`	logical; whether the calculation should give feedback
`partial_decomp`	logical; if `TRUE`, the function uses the RSpectra package to more quickly calculate the eigen-decomposition. This is usually faster than standard eigen-decomponsition when `ncol(x) > 100` and `k` is small
`max_iters`	number of maximum iterations
`conv_criteria`	convergence criteria. The difference between average deviance in successive iterations
`random_start`	logical; whether to randomly inititalize the parameters. If `FALSE`, function will use an eigen-decomposition as starting value
`start_U`	starting value for the orthogonal matrix
`start_mu`	starting value for mu. Only used if `main_effects = TRUE`
`main_effects`	logical; whether to include main effects in the model
`validation`	optional validation matrix. If supplied and `m = 0`, the validation data is used to solve for `m`
`M`	depricated. Use `m` instead
`use_irlba`	depricated. Use `partial_decomp` instead

Value

An S3 object of class lpca which is a list with the following components:

`mu`	the main effects
`U`	a `k`-dimentional orthonormal matrix with the loadings
`PCs`	the princial component scores
`m`	the parameter inputed or solved for
`iters`	number of iterations required for convergence
`loss_trace`	the trace of the average negative log likelihood of the algorithm. Should be non-increasing
`prop_deviance_expl`	the proportion of deviance explained by this model. If `main_effects = TRUE`, the null model is just the main effects, otherwise the null model estimates 0 for all natural parameters.

References

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

# Logistic PCA likely does a better job finding latent features
# than standard PCA
plot(svd(mat_logit)$u[, 1], lpca$PCs[, 1])
plot(svd(mat_logit)$u[, 1], svd(mat)$u[, 1])
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

# Logistic PCA likely does a better job finding latent features
# than standard PCA
plot(svd(mat_logit)$u[, 1], lpca$PCs[, 1])
plot(svd(mat_logit)$u[, 1], svd(mat)$u[, 1])

Logistic Singular Value Decomposition

Description

Dimensionality reduction for binary data by extending SVD to minimize binomial deviance.

Usage

logisticSVD(
  x,
  k = 2,
  quiet = TRUE,
  max_iters = 1000,
  conv_criteria = 1e-05,
  random_start = FALSE,
  start_A,
  start_B,
  start_mu,
  partial_decomp = TRUE,
  main_effects = TRUE,
  use_irlba
)
logisticSVD(
  x,
  k = 2,
  quiet = TRUE,
  max_iters = 1000,
  conv_criteria = 1e-05,
  random_start = FALSE,
  start_A,
  start_B,
  start_mu,
  partial_decomp = TRUE,
  main_effects = TRUE,
  use_irlba
)

Arguments

`x`	matrix with all binary entries
`k`	rank of the SVD
`quiet`	logical; whether the calculation should give feedback
`max_iters`	number of maximum iterations
`conv_criteria`	convergence criteria. The difference between average deviance in successive iterations
`random_start`	logical; whether to randomly inititalize the parameters. If `FALSE`, algorithm will use an SVD as starting value
`start_A`	starting value for the left singular vectors
`start_B`	starting value for the right singular vectors
`start_mu`	starting value for mu. Only used if `main_effects = TRUE`
`partial_decomp`	logical; if `TRUE`, the function uses the RSpectra package to more quickly calculate the SVD. When the number of columns is small, the approximation may be less accurate and slower
`main_effects`	logical; whether to include main effects in the model
`use_irlba`	depricated. Use `partial_decomp` instead

Value

An S3 object of class lsvd which is a list with the following components:

`mu`	the main effects
`A`	a `k`-dimentional orthogonal matrix with the scaled left singular vectors
`B`	a `k`-dimentional orthonormal matrix with the right singular vectors
`iters`	number of iterations required for convergence
`loss_trace`	the trace of the average negative log likelihood of the algorithm. Should be non-increasing
`prop_deviance_expl`	the proportion of deviance explained by this model. If `main_effects = TRUE`, the null model is just the main effects, otherwise the null model estimates 0 for all natural parameters.

References

de Leeuw, Jan, 2006. Principal component analysis of binary data by iterated singular value decomposition. Computational Statistics & Data Analysis 50 (1), 21–39.

Collins, M., Dasgupta, S., & Schapire, R. E., 2001. A generalization of principal components analysis to the exponential family. In NIPS, 617–624.

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

# Logistic SVD likely does a better job finding latent features
# than standard SVD
plot(svd(mat_logit)$u[, 1], lsvd$A[, 1])
plot(svd(mat_logit)$u[, 1], svd(mat)$u[, 1])
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

# Logistic SVD likely does a better job finding latent features
# than standard SVD
plot(svd(mat_logit)$u[, 1], lsvd$A[, 1])
plot(svd(mat_logit)$u[, 1], svd(mat)$u[, 1])

Plot convex logistic PCA

Description

Plots the results of a convex logistic PCA

Usage

## S3 method for class 'clpca'
plot(x, type = c("trace", "loadings", "scores"), ...)
## S3 method for class 'clpca'
plot(x, type = c("trace", "loadings", "scores"), ...)

Arguments

`x`	convex logistic PCA object
`type`	the type of plot `type = "trace"` plots the algorithms progress by iteration, `type = "loadings"` plots the first 2 PC loadings, `type = "scores"` plots the first 2 PC scores
`...`	Additional arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run convex logistic PCA on it
clpca = convexLogisticPCA(mat, k = 2, m = 4, main_effects = FALSE)

## Not run: 
plot(clpca)

## End(Not run)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run convex logistic PCA on it
clpca = convexLogisticPCA(mat, k = 2, m = 4, main_effects = FALSE)

## Not run: 
plot(clpca)

## End(Not run)

Plot CV for logistic PCA

Description

Plot cross validation results logistic PCA

Usage

## S3 method for class 'cv.lpca'
plot(x, ...)
## S3 method for class 'cv.lpca'
plot(x, ...)

Arguments

`x`	a `cv.lpca` object
`...`	Additional arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lpca(dat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lpca(dat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)

Plot logistic PCA

Description

Plots the results of a logistic PCA

Usage

## S3 method for class 'lpca'
plot(x, type = c("trace", "loadings", "scores"), ...)
## S3 method for class 'lpca'
plot(x, type = c("trace", "loadings", "scores"), ...)

Arguments

`x`	logistic PCA object
`type`	the type of plot `type = "trace"` plots the algorithms progress by iteration, `type = "loadings"` plots the first 2 principal component loadings, `type = "scores"` plots the loadings first 2 principal component scores
`...`	Additional arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 2, m = 4, main_effects = FALSE)

## Not run: 
plot(lpca)

## End(Not run)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 2, m = 4, main_effects = FALSE)

## Not run: 
plot(lpca)

## End(Not run)

Plot logistic SVD

Description

Plots the results of a logistic SVD

Usage

## S3 method for class 'lsvd'
plot(x, type = c("trace", "loadings", "scores"), ...)
## S3 method for class 'lsvd'
plot(x, type = c("trace", "loadings", "scores"), ...)

Arguments

`x`	logistic SVD object
`type`	the type of plot `type = "trace"` plots the algorithms progress by iteration, `type = "loadings"` plots the first 2 principal component loadings, `type = "scores"` plots the loadings first 2 principal component scores
`...`	Additional arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 2, main_effects = FALSE, partial_decomp = FALSE)

## Not run: 
plot(lsvd)

## End(Not run)
# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 2, main_effects = FALSE, partial_decomp = FALSE)

## Not run: 
plot(lsvd)

## End(Not run)

Predict Convex Logistic PCA scores or reconstruction on new data

Description

Predict Convex Logistic PCA scores or reconstruction on new data

Usage

## S3 method for class 'clpca'
predict(object, newdata, type = c("PCs", "link", "response"), ...)
## S3 method for class 'clpca'
predict(object, newdata, type = c("PCs", "link", "response"), ...)

Arguments

`object`	convex logistic PCA object
`newdata`	matrix with all binary entries. If missing, will use the data that `object` was fit on
`type`	the type of fitting required. `type = "PCs"` gives the PC scores, `type = "link"` gives matrix on the logit scale and `type = "response"` gives matrix on the probability scale
`...`	Additional arguments

Examples

# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
clpca = convexLogisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

PCs = predict(clpca, mat_new)
# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
clpca = convexLogisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

PCs = predict(clpca, mat_new)

Predict Logistic PCA scores or reconstruction on new data

Description

Predict Logistic PCA scores or reconstruction on new data

Usage

## S3 method for class 'lpca'
predict(object, newdata, type = c("PCs", "link", "response"), ...)
## S3 method for class 'lpca'
predict(object, newdata, type = c("PCs", "link", "response"), ...)

Arguments

`object`	logistic PCA object
`newdata`	matrix with all binary entries. If missing, will use the data that `object` was fit on
`type`	the type of fitting required. `type = "PCs"` gives the PC scores, `type = "link"` gives matrix on the logit scale and `type = "response"` gives matrix on the probability scale
`...`	Additional arguments

Examples

# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

PCs = predict(lpca, mat_new)
# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

PCs = predict(lpca, mat_new)

Predict Logistic SVD left singular values or reconstruction on new data

Description

Predict Logistic SVD left singular values or reconstruction on new data

Usage

## S3 method for class 'lsvd'
predict(
  object,
  newdata,
  quiet = TRUE,
  max_iters = 1000,
  conv_criteria = 1e-05,
  random_start = FALSE,
  start_A,
  type = c("PCs", "link", "response"),
  ...
)
## S3 method for class 'lsvd'
predict(
  object,
  newdata,
  quiet = TRUE,
  max_iters = 1000,
  conv_criteria = 1e-05,
  random_start = FALSE,
  start_A,
  type = c("PCs", "link", "response"),
  ...
)

Arguments

`object`	logistic SVD object
`newdata`	matrix with all binary entries. If missing, will use the data that `object` was fit on
`quiet`	logical; whether the calculation should give feedback
`max_iters`	number of maximum iterations
`conv_criteria`	convergence criteria. The difference between average deviance in successive iterations
`random_start`	logical; whether to randomly inititalize the parameters. If `FALSE`, algorithm implicitly starts `A` with 0 matrix
`start_A`	starting value for the left singular vectors
`type`	the type of fitting required. `type = "PCs"` gives the left singular vectors, `type = "link"` gives matrix on the logit scale and `type = "response"` gives matrix on the probability scale
`...`	Additional arguments

Details

Minimizes binomial deviance for new data by finding the optimal left singular vector matrix (A), given B and mu. Assumes the columns of the right singular vector matrix (B) are orthonormal.

Examples

# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

A_new = predict(lsvd, mat_new)
# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

A_new = predict(lsvd, mat_new)

Project onto the Fantope

Description

Project a symmetric matrix onto the convex set of the rank k Fantope

Usage

project.Fantope(x, k, partial_decomp = FALSE)
project.Fantope(x, k, partial_decomp = FALSE)

Arguments

`x`	a symmetric matrix
`k`	the rank of the Fantope desired
`partial_decomp`	logical; if `TRUE`, the function uses the RSpectra package to quickly calculate the eigendecomposition when `ncol(x)` is large and `k` is small

Value

`H`	a rank `k` Fantope matrix
`U`	a `k`-dimentional orthonormal matrix with the first `k` eigenvectors of `H`
`rank`	the rank of the Fantope matrix `H`

Package 'logisticPCA'

Help Index

logisticPCA-package

Description

Author(s)

Convex Logistic Principal Component Analysis

Description

Usage

Arguments

Value

References

Examples

CV for convex logistic PCA

Description

Usage

Arguments

Value

Examples

CV for logistic PCA

Description

Usage

Arguments

Value

Examples

CV for logistic SVD

Description

Usage

Arguments

Value

Examples

Fitted values using logistic PCA

Description

Usage

Arguments

Examples

Fitted values using logistic SVD

Description

Usage

Arguments

Examples

United States Congressional Voting Records 1984

Description

Usage

Format

Source

Examples

Inverse logit for matrices

Description

Usage

Arguments

Examples

Bernoulli Log Likelihood

Description

Usage

Arguments

Logistic Principal Component Analysis

Description

Usage

Arguments

Value

References

Examples

Logistic Singular Value Decomposition

Description

Usage

Arguments

Value

References

Examples

Plot convex logistic PCA

Description

Usage

Arguments

Examples

Plot CV for logistic PCA

Description

Usage

Arguments

Examples

Plot logistic PCA