# PLS Path Modeling Based on Formula

### Description

This fonction estimate PLS Path Models specified using formula. The formulas using for the inner models and the outer models must respect the forms describe in the details section.

### Usage

1 2 3 |

### Arguments

`Formula ` |
A string describe the the inner and outer model using formulas. The inner models are describe using "=~" and "~~" for the inner model. (see details and exemple) |

`Data ` |
matrix or data frame containing the manifest variables. |

`modes ` |
character vector indicating the type of measurement for each block. Possible values are: "A", "B", "newA", "PLScore", "PLScow". The length of modes must be equal to the length of blocks. |

`scaling ` |
optional argument for runing the non-metric approach; it is a list of string vectors indicating the type of measurement scale for each manifest variable specified in blocks. scaling must be specified when working with non-metric variables. Possible values: "num" (linear transformation, suitable for numerical variables), "raw" (no transformation), "nom" (non-monotonic transformation, suitable for nominal variables), and "ord" (monotonic transformation, suitable for ordinal variables). |

`scheme ` |
string indicating the type of inner weighting scheme. Possible values are "centroid", "factorial", or "path". |

`scaled ` |
whether manifest variables should be standardized. Only used when scaling = NULL. When (TRUE, data is scaled to standardized values (mean=0 and variance=1). The variance is calculated dividing by N instead of N-1). |

`tol ` |
decimal value indicating the tolerance criterion for the iterations (tol=0.000001). Can be specified between 0 and 0.001. |

`maxiter ` |
integer indicating the maximum number of iterations (maxiter=100 by default). The minimum value of maxiter is 100. |

`plscomp ` |
optional vector indicating the number of PLS components (for each block) to be used when handling non-metric data (only used if scaling is provided) |

`boot.val ` |
whether bootstrap validation should be performed. (FALSE by default). |

`br ` |
number bootstrap resamples. Used only when boot.val=TRUE. When boot.val=TRUE, the default number of re-samples is 100. |

`dataset ` |
whether the data matrix used in the computations should be retrieved (TRUE by default). |

`plot.outer ` |
Boolean specify if yes (plot.outer=TRUE) or not (plot.outer=FALSE) the outer plot may be printed. (FALSE by default). |

`plot.inner ` |
Boolean specify if yes (plot.inner=TRUE) or not (plot.inner=FALSE) the outer plot may be printed. (TRUE by default). |

### Details

The function plspm.formula estimates a path model by partial least squares approach providing the full set of results as the plspm function of the 'plspm' package. The algorithm compute itself the path matrix and the blocks list. To do that, the model must be specify using the two rules below:

`LatVar1 =~ ManVar1+ManVar2+ManVar3`

Description of the relation between the latent variable (LatVar1) and its manifests variables (ManVar1, ManVar2 and ManVar3

`LatVar3 ~~ LatVar1+LatVar2`

Description of the relation between the latent variable (LatVar3) and the other latents variables (LatVar1 and ManVar2) linked to that variable

All the formulars must be in a single string with a newline as separator. Phisical new lines are generally used (see example).

### Value

The result of the 'plspm.formula' is an objet of class 'plspm'. The return values are the same of the plspm fonction in the 'plspm' package.

### Note

The formula approach of the PLS Path Modeling is need for the developement of the resilometric. Resilometrics is a new discipline under development for computational modeling of the resilience processes.

### Author(s)

ACHIEPO Odilon Yapo M. <kingodilon@gmail.com>

### References

Gaston Sanchez, Laura Trinchera and Giorgio Russolillo (2015). plspm: Tools for Partial Least Squares Path Modeling (PLS-PM). R package version 0.4.7. http://CRAN.R-project.org/package=plspm

### See Also

`plspm.params`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
## Load data (satisfaction data in plspm package)
data("plspmsat")
## Model specification by formulas
satmodele <- "
## measure model specification
EXPE =~ expe1+expe2+expe3+expe4+expe5
IMAG =~ imag1+imag2+imag3+imag4+imag5
LOY =~ loy1+loy2+loy3+loy4
SAT =~ sat1+sat2+sat3+sat4
VAL =~ val1+val2+val3+val4
QUAL =~ qual1+qual2+qual3+qual4+qual5
## outer model specification
EXPE ~~ IMAG
LOY ~~ IMAG+SAT
SAT ~~ IMAG+EXPE+QUAL+VAL
VAL ~~ EXPE+QUAL
QUAL ~~ EXPE
"
## estimation modes of latent's blocks
satmodes <- rep("A",6)
## PLSPM model estimation using formula
satres.plspm <- plspm.formula(Formula = satmodele, Data = plspmsat,
modes = satmodes, plot.outer = TRUE,
plot.inner = TRUE, scaled = FALSE)
``` |