LogBip {BiplotML} R Documentation

## Fitting a Binary Logistic Biplot using optimization methods

### Description

This function estimates the vector μ, matrix A and matrix B using the optimization algorithm chosen by the user and applies a bootstrap methodology to determine the confidence ellipses.

### Usage

```LogBip(
x,
k = 2,
method = "MM",
type = NULL,
plot = TRUE,
maxit = NULL,
endsegm = 0.9,
label.ind = FALSE,
col.ind = NULL,
draw = c("biplot", "ind", "var"),
random_start = FALSE,
truncated = TRUE,
L = 0
)
```

### Arguments

 `x` Binary matrix. `k` Dimensions number. By default `k = 2`. `method` Method to be used to estimate the parameters. By default `method="CG"` `type` For the conjugate-gradients method. Takes value 1 for the Fletcher–Reeves update, 2 for Polak–Ribiere and 3 for Beale–Sorenson. `plot` Plot the Bootstrap Logistic Biplot. `maxit` The maximum number of iterations. Defaults to 100 for the gradient methods, and 500 without gradient. `endsegm` The segment starts at 0.5 and ends at this value. By default `endsegm = 0.90`. `label.ind` By default the row points are not labelled. `col.ind` Color for the rows marks. `draw` The graph to draw ("ind" for the individuals, "var" for the variables and "biplot" for the row and columns coordinates in the same graph) `random_start` Logical value; whether to randomly inititalize the parameters. If `FALSE`, algorithm will use an SVD as starting value. `truncated` Find the k largest singular values and vectors of a matrix. `L` Penalization parameter. By default `L = 0`.

### Details

The methods that can be used to estimate the parameters of a logistic biplot

- For methods based on the conjugate gradient use method = "CG" and

- type = 1 for the Fletcher Reeves. - type = 2 for Polak Ribiere. - type = 3 for Hestenes Stiefel. - type = 4 for Dai Yuan.

- To use the iterative coordinate descendent MM algorithm then method = "MM".

- To use the BFGS formula, method = "BFGS".

### Value

Coordenates of the matrix A and B, threshold for classification rule

### Author(s)

Giovany Babativa <gbabativam@gmail.com>

### References

Babativa-Marquez, J.G. and Vicente-Villardon, J.L. (2021). Logistic biplot by conjugate gradient algorithms and iterated SVD. Mathematics 2021.

John C. Nash (2011). Unifying Optimization Algorithms to Aid Software System Users:optimx for R. Journal of Statistical Software. 43(9). 1–14.

John C. Nash (2014). On Best Practice Optimization Methods in R. Journal of Statistical Software. 60(2). 1–14.

Nocedal, J.;Wright, S. (2006). Numerical optimization; Springer Science & Business Media.

Vicente-Villardon, J.L. and Galindo, M. Purificacion (2006), Multiple Correspondence Analysis and related Methods. Chapter: Logistic Biplots. Chapman-Hall

`plotBLB, pred_LB, fitted_LB`
```