| Type: | Package |
| Title: | Path Coefficient Analysis |
| Version: | 0.1 |
| Date: | 2024-9-12. |
| Author: | Ali Arminian 
[aut, cre, cph] |
| Maintainer: | Ali Arminian <abeyran@gmail.com> |
| Description: | Facilitates the performance of several analyses, including simple and sequential path coefficient analysis, correlation estimate, drawing correlogram, Heatmap, and path diagram. When working with raw data, that includes one or more dependent variables along with one or more independent variables are available, the path coefficient analysis can be conducted. It allows for testing direct effects, which can be a vital indicator in path coefficient analysis. The process of preparing the dataset rule is explained in detail in the vignette file "Path.Analysis_manual.Rmd". You can find this in the folders labelled "data" and "~/inst/extdata". Also see: 1)the 'lavaan', 2)a sample of sequential path analysis in 'metan' suggested by Olivoto and Lúcio (2020) <doi:10.1111/2041-210X.13384>, 3)the simple 'PATHSAS' macro written in 'SAS' by Cramer et al. (1999) <doi:10.1093/jhered/90.1.260>, and 4)the semPlot() function of 'OpenMx' as initial tools for conducting path coefficient analyses and SEM (Structural Equation Modeling). To gain a comprehensive understanding of path coefficient analysis, both in theory and practice, see a 'Minitab' macro developed by Arminian, A. in the paper by Arminian et al. (2008) <doi:10.1080/15427520802043182>. |
| License: | GPL-3 |
| URL: | https://github.com/abeyran/Path.Analysis |
| BugReports: | https://github.com/abeyran/Path.Analysis/issues |
| Depends: | R (≥ 4.1.0) |
| Imports: | stats, corrr, corrplot, Hmisc, gplots, mathjaxr, pastecs, graphics, grDevices, DiagrammeR, ComplexHeatmap, metan |
| Suggests: | car, ggplot2, devtools, usethis, testthat, knitr, rmarkdown, roxygen2, spelling |
| VignetteBuilder: | knitr |
| RdMacros: | mathjaxr |
| Encoding: | UTF-8 |
| Copyright: | Ali Arminian |
| RoxygenNote: | 7.3.2 |
| Language: | en-US |
| LazyData: | true |
| LazyLoad: | true |
| NeedsCompilation: | no |
| BuildManual: | TRUE |
| Packaged: | 2024-09-23 19:30:28 UTC; Administrator |
| Repository: | CRAN |
| Date/Publication: | 2024-09-25 08:20:05 UTC |
Path Coefficient Analysis
Description
Path.Analysis does descriptive statistics on dataset and importantly graphical representation of data such as drawing heatmaps, correlogram and path diagram.
Author(s)
Ali Arminian abeyran@gmail.com
See Also
Useful links:
Report bugs at https://github.com/abeyran/Path.Analysis/issues
Drawing the correlogram
Description
![[Stable]](./figures/lifecycle-stable.svg)
-
corr_plot()draws a correlogram for data
Usage
cor_plot(datap)
Arguments
datap |
The data set |
Value
Returns an object of class gg, ggmatrix.
Author(s)
Ali Arminian abeyran@gmail.com
References
Olivoto, T, and A Dal’Col Lúcio. 2020. “Metan: An r Package for Multi‐environment Trial Analysis.” Methods in Ecology and Evolution, 11(6): 783–89. https://doi.org/10.1111/2041-210 X.13384.
See Also
correlogram, diagram, and lavaan package for drawing path diagrams.
Examples
data(dtsimp)
cor_plot(dtsimp)
Correlation Analysis
Description
-
corr()estimates Pearson correlation coefficients among parametric numerical characteristics as follows: -
The Pearson correlation coefficient:\[ r_{x,y} = \frac{n\sum{xy}-(\sum{x})(\sum{y})} {\sqrt{(n\sum{x^2}-(\sum{x})^2)(n\sum{y^2}-(\sum{y})^2)}}\]
or: \[ r_{x,y} =\frac{\Sigma(x-\bar{x})(y-\bar{y})} {\sqrt{\Sigma{(x-\bar{x})^2\Sigma(y-\bar{y}})^2}} \]
where \(r_{x,y}\) is the correlation coefficient
between \(x\) and \(y\) variables.
Usage
corr(datap, verbose = FALSE)
Arguments
datap |
The data set |
verbose |
If |
Details
The corr() function estimates correlation coefficients
and their significance in the form of a table of one or
more independent (exogenous) variables on a dependent
(endogenous) variable along with testing the significance.
Value
Returns a list of two objects:
- Correlations
the data frame of Pearson's correlation coefficients
- P_values
the data frame of significance of correlation coefficients (r):
pp-value for testing the rlowCIlower confidence interval of ruppCIupper confidence interval of r
Author(s)
Ali Arminian abeyran@gmail.com
See Also
correlation
Examples
data(dtsimp)
corr(dtsimp, verbose = FALSE)
data(dtraw)
corr(dtraw[, -1], verbose = FALSE)
Data preparation
Description
![[Experimental]](./figures/lifecycle-experimental.svg)
Prepares data for analyses
Usage
dataprep(datap)
Arguments
datap |
dataset |
Value
Returns a data frame
Descriptive statistics
Description
-
desc()estimates the descriptive statistics such asMin(Minimum),1st Qu.(quartile),Median,Mean(average),3rd Qu.(3rd quartile),Max(maximum),var(variance),std.dev(standard deviation),coef.var(CV or coefficient of variation) of the data set.
Usage
desc(datap, resp)
Arguments
datap |
The data set |
resp |
an integer value indicating the column
in |
Details
The desc() function estimates the descriptive statistics,
in tables for one or more independent (exogenous) variables on
a dependent(endogenous) variable. It acts only on numerical
variables.
For example for the variable x:
-
1st. quartile:\[Q_1 = (n + 1) x 1/4\] -
2nd. quartile or Median:\[md = (n + 1) x 2/4\] -
3rd Qu.:\[Q_3 = (n + 1) x 3/4\] -
Arithmetic mean:\[\bar{x}=\frac{1}{n} \sum_{i=i}^{n} x_{i}\] -
Range:\[R_x = \max(x) - \min(x)\] -
Variance: \[\sigma_{x}^2 = \frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n} \] -
Standard deviation:\[sd_x = \sqrt{\frac{\sum_{i} (x_{i} - \mu)^2}{n}}\] -
SEM or SE.mean, the standard error of the mean is calculated simply by taking the standard deviation and dividing it by the square root of the sample size: \[SEM_x = \frac{sd(x)}{\sqrt{n}}\] -
coef.var or coefficient of variation:\[CV = \frac{sd(x)}{\bar{x} }\times 100\]
Value
Returns a list of 3 objects:
- desc1
Descriptive statistics1 of input data
- desc2
Descriptive statistics2 of input data
- corcf
A table of correlation coefficients
Author(s)
Ali Arminian abeyran@gmail.com
References
Bhattacharyya GK and Johnson RA 1997. Statistical Concepts and Methods, John Wiley and Sons, New York.
Draper N and Smith H 1981. Applied Regression Analysis, John Wiley & Sons, New York.
Neter, J, Whitmore, GA, Wasserman, W 1992. Applied Statistics. Allyn & Bacon, Incorporated, ISBN 10: 0205134785 / ISBN 13: 9780205134786.
Snedecor, G.W., Cochran, W.G. 1980. Statistical Methods. Iowa State University Press.
See Also
correlation, multiple linear regression,
Examples
data(dtsimp)
desc(dtsimp, 1)
data(dtraw)
desc(dtraw[, -1], 1)
data(heart)
desc(heart, 2)
Dataset 2: a number of 9 traits measured on 35 Camelina DH lines.
Description
Dataset 2: a number of 9 traits measured on 35 Camelina DH lines.
Usage
data(dtraw)
Format
A data.frame with 35 observations of 9 variables.
DH linesa character vector
ya numeric vector
X1a numeric vector
X2a numeric vector
X3a numeric vector
X4a numeric vector
X5a numeric vector
X6a numeric vector
X7a numeric vector
X8a numeric vector
Examples
library(Path.Analysis)
data(dtraw)
Dataset 3: a number of 9 traits measured on 35 Camelina DH lines.
Description
Dataset 3: a number of 9 traits measured on 35 Camelina DH lines.
Usage
data(dtraw2)
Format
A data.frame with 35 observations of 9 variables.
DH linesa character vector considered as rownames
ya numeric vector
X1a numeric vector
X2a numeric vector
X3a numeric vector
X4a numeric vector
X5a numeric vector
X6a numeric vector
X7a numeric vector
X8a numeric vector
Examples
library(Path.Analysis)
data(dtraw2)
Dataset 4: a dataframe consisting of 7 variables measured on 8 observations.
Description
Dataset 4: a dataframe consisting of 7 variables measured on 8 observations.
Usage
data(dtseq)
Format
A data.frame with 8 observations of 7 variables.
Genotypesa character vector
YLDa numeric vector
DFTa numeric vector
FSa numeric vector
FVa numeric vector
FWa numeric vector
DFLa numeric vector
FLPa numeric vector
Examples
library(Path.Analysis)
data(dtseq)
Dataset5
Description
Dataset5
Usage
data(dtseqr)
Format
A data.frame with 24 observations of 7 variables.
Genotypesa character vector
Repa numeric vector
YLDa numeric vector
DFTa numeric vector
FSa numeric vector
FVa numeric vector
FWa numeric vector
DFLa numeric vector
FLPa numeric vector
Examples
library(Path.Analysis)
data(dtseqr)
Dataset 1: a dependent (y) and 3 independent(x1 to x3) variables.
Description
Dataset 1: a dependent (y) and 3 independent(x1 to x3) variables.
Usage
data(dtsimp)
Format
A data.frame with 105 observations of 4 variables.
ya numeric vector
x1a numeric vector
x2a numeric vector
x3a numeric vector
Examples
library(Path.Analysis)
data(dtsimp)
Dataset 6: Heart Disease data set
Description
A mixed variable dataset containing 14 variables of 297 patients for their heart disease diagnosis.
Usage
data(heart)
Format
A data.frame including 297 rows and 14 variables:
- age
Age in years (numerical).
- sex
Sex: 1 = male, 0 = female (logical).
heart.diseasea numeric vector as dependent.
bikinga numeric vector as the first independent.
smokinga numeric vector as the 2nd independent.
Source
The data set is belong to machine learning repository of UCI. The original data set includes 303 patients with 6 NA's. After removing missing values, it reduced into 297 patients.
https://archive.ics.uci.edu/ml/datasets/Heart+Disease
References
Lichman, M. (2013). UCI machine learning repository.
Examples
library(Path.Analysis)
data(heart)
Creating the Heatmap chart
Description
-
heat_map()draws a double-clusteredheatmapfor path coefficients analysis. Please be cautious that this function acts only on numeric variables/columns (see example ondtraw2data set). Users for drawing other types of heatmaps may useheatmap.3,ComplexHeatmapandpheatmapR packages. Where an example is given in the vignette manual of this package (Path.Analysis_manual.Rmd)
Usage
heat_map(datap)
Arguments
datap |
The data set |
Value
Returns an object of class heatmap.2.
Author(s)
Ali Arminian abeyran@gmail.com
See Also
lavaan and diagram packages for drawing path diagrams.
Examples
data(dtraw2)
dtraw2 <- scale(as.data.frame(dtraw2))
heat_map(dtraw2)
Direct and Indirect Effects Matrices and Diagram
Description
-
matdiag()extracts the direct effect and indirect effects matrices of data in path analysis along with the significance of direct effects where direct effects are shown as a vector (columnar matrix of 1*n dimensions and indirect effects are off-diagonal effects. Later, draws a diagram for path coefficient analysis based on theDiagrammeRpackage.
Usage
matdiag(datap, resp, verbose = FALSE)
Arguments
datap |
The data set |
resp |
The response variable |
verbose |
If |
Details
The matdiag function estimates the direct and indirect effects in path
coefficient analysis as tables along with drawing the diagram of path analysis.
This is apparently the only program testing the significance of direct effects
in a path analysis. Note: all variables must be numeric for matrix calculations
and the next plotting.
In a path model, path coefficients or direct effects (Pi's) indicate the direct effects of a variable on another, and are standardized partial regression coefficients (in Wright's terminology) due they are estimated from correlations or from the transformed (standardized) data as:
The path equations are as follows:
One dependent variable: \[P_1 + P_2r_{12} + P_3r_{13} + ... + P_nr_{1n} = rY_1\] \[P_1r_{21} + P_2 + P_3r_{23} + ... + P_nr_{2n} = rY_2\] \[...\] \[P_1rn_1 + P_2r_{n2} + P_3r_{n3} + ... + P_n = rY_n\]
Extension to more dependent variables:
Path.Analysisis capable of performing this straightforward function through detailed explanations. The linear regression model with a single response in its form is as follows (Johnson and Wichern (2007): \(Y = \beta_0 + \beta_1Z_1 + ... + \beta_rZ_r + \epsilon\)where the multivariate multiple linear regression model is as follows: \[Y_1 = \beta_0 + \beta_1Z_{11} + \beta_2Z{12} + ... + \beta_rZ_{1r} + \epsilon_1\] \[Y_2 = \beta_0 + \beta_1Z_{21} + \beta_2Z{22} + ... + \beta_rZ_{2r} + \epsilon_2\] \[...\] \[Y_n = \beta_0 + \beta_1Z_{n1} + \beta_2Z{n2} + ... + \beta_rZ_{nr} + \epsilon_n\]
As stated by Bondari (1990), for two dependent variables \(Y_1\) and \(Y_2\): \[ Y_1 = p_1X_1 + p_2X_2 + p_3X_3 + ... + p_nX_n \] \[ Y_2 = p'_1X_1 + p'_2X_2 + p'_3X_3 + ... + p'_nX_n \] \[ ... \]
where: \[ r_{Y_1Y_2} = p_1p'_1 + p_2p'_2 + p_3p'_3 + ... + p_np'_n + \sigma_{i=j}p_ip'_1r_{ij} = \sigma_{i,j}p_ip'_ir_{ij} \]
Value
Returns a list with three objects
- direff
a data frame of direct effects
- matall
a matrix of direct and indirect effects
- Residual
a constant of residuals
Author(s)
Ali Arminian abeyran@gmail.com
References
Arminian, A, MS Kang, M Kozak, S Houshmand, and P Mathews. 2008. “MULTPATH: A Comprehensive Minitab Program for Computing Path Coefficients and Multiple Regression for Multivariate Analyses.” Journal of Crop Improvement, 22(1): 82–120.
Bondari, K. 1990. "PATH ANALYSIS IN AGRICULTURAL RESEARCH," Conference on Applied Statistics in Agriculture. https://do i.org/10.4148/2475-7772.1439
Cramer, C.S, TC Wehner, and SB Donaghy. 1999. “PATHSAS: A SAS Computer Program for Path Coefficient Analysis of Quantitative Data.” Journal of Heredity, 90(1): 260–62. https://doi.org/10 .1093/jhered/90.1.260.
Johnson, R.A., Wichern, D.W. 2007. Applied Multivariate Statistical Analysis. Prentice Hall, USA.
Li, C.C. 1975. Path Analysis: A Primer. Boxwood Pr. 346 p.
Olivoto, T, and A Dal’Col Lúcio. 2020. “Metan: An r Package for Multi‐environment Trial Analysis.” Methods in Ecology and Evolution, 11(6): 783–89. https://doi.org/10.1111/2041-210 X.13384.
Wolfle, LM. 2003. “The Introduction of Path Analysis to the Social Sciences, and Some Emergent Themes: An Annotated Bibliography.” Structural Equation Modeling, 10(1): 1–34.
Wright, S. 1923. “The Theory of Path Coefficients a Reply to Niles’s Criticism.” Genetics, 8(3): 239.
———. 1934. “The Method of Path Coefficients.” The Annals of Mathematical Statistics, 5(3): 161–215.
———. 1960. “Path Coefficients and Path Regressions: Alternative or Complementary Concepts?” Biometrics, 16(2): 189–202.
See Also
correlation, multiple linear regression,
and matrix notations in mathematics.
lavaan and diagrammeR packages for
drawing path diagrams
Examples
data(dtsimp)
matdiag(dtsimp, 1, verbose = FALSE)
data(dtraw)
matdiag(dtraw[, -1], 1, verbose = FALSE)
data(heart)
matdiag(heart, 2, verbose = FALSE)
Network plot
Description
-
network.plot()draws the network plot of path coefficients analysis
Usage
network.plot(datap)
Arguments
datap |
The data set |
Details
The network.plot() draws a correlogram and a heatmap
for data, if requested by user
Value
Returns an object of class network_plot.
Author(s)
Ali Arminian abeyran@gmail.com
References
Kuhn et al. 2022. corrr package. doi: <10.32614/CRAN.package.corrr> https://github.com/tidymodels/corrr
See Also
correlogram, diagram, and lavaan packages
for drawing path diagrams.
Examples
data(dtraw2)
network.plot(dtraw2)
Multiple Linear Regression
Description
-
reg()performs a multiple linear regression analysis with extracting the attributed parameters
Usage
reg(datap, resp, verbose = FALSE)
Arguments
datap |
The data set |
resp |
an integer value indicating the column in |
verbose |
If |
Details
The reg function fits a multiple linear regression analysis
of one or more independent (exogenous) variables on a dependent(endogenous)
variable in a linear pattern along with testing the significance of
parameters. It is important that according to the type of data may produce some warning errors e.g., for dtsimp as:
Warning message: In summary.lm(mlreg): essentially perfect fit: summary may be unreliable.
This case is due to the intrinsic characteristics of data
Value
An object of class list
Author(s)
Ali Arminian abeyran@gmail.com
See Also
multiple linear regression
Examples
data(dtsimp)
reg(dtsimp, 1, verbose = FALSE)
data(heart)
reg(heart, 1, verbose = FALSE)