Path and Variance Covariance Analysis

Path analysis is an extension of the regression model, used to test the fit of the correlation matrix against two or more causal models. The model is typically represented by a circle-and-arrow diagram, where single arrows indicate causation. A regression is done for each variable as a dependent on others identified as causes in the model. The regression weights predicted by the model are compared with the observed correlation matrix, and a goodness-of-fit statistic is calculated. The best-fitting model is selected by the researcher for theoretical advancement.

Data Arrangement in the Data File

• Un-replicated data: The data arrangement is similar to that of Correlation and Regression Analysis.
• Correlation Matrix: The correlation matrix is entered either in the data file or in the text area of the web page.
• Replicated data: The characters under study are laid out horizontally, while replication within treatments is arranged vertically. The first replication of the first treatment of all characters is entered in the first line, separated by spaces or tabs, followed by subsequent replications. Enter the second treatment's replications in the next lines, and continue similarly for all treatments.

Example Data Arrangement

For 10 genotypes, 3 replications, and 8 characters, the data arrangement is as follows:

        C1      C2     C3     C4     C5      C6       C7        C8
G1R1
G1R2
G1R3
G2R1
G2R2
G2R3
G3R1
G3R2
G3R3
G4R1
G4R2
G4R3
G5R1
G5R2
G5R3
G6R1
G6R2
G6R3
G7R1
G7R2
G7R3
G8R1
G8R2
G8R3
G9R1
G9R2
G9R3
G10R1
G10R2
G10R3

Example Data Arrangement

This is an example dataset containing 10 genotypes (G1 to G10) and 3 replications (R1 to R3) for each genotype. The dataset includes three variables: Yield, Tillers, and Root Length.

The data is structured with the replications of each genotype as separate entries. The first column indicates the replication for each genotype, while the remaining columns represent the variables under study.

36.4	33.5	38.5
41.3	40.1	43
51.7	47.4	40.6
22.6	20.3	36.5
39.4	28.6	37.4
30.2	29.5	30.8
21.8	25.5	27.1
26.4	21.5	25.8
22.6	32.8	28
31.2	21.3	27.9
25.4	33.7	25.9
23.7	34.7	27.2
24.3	32.3	22
34.3	28.1	28.2
36.5	28.2	38.7
40	41.3	38.6
38.9	43.6	29.6
37.1	39.5	28.6
42.6	38.3	31.7
28.2	35.4	21
29.5	47.6	30.1
27.1	28.5	25.4
27.7	29.6	17.3
17.7	25.8	24.8
20.2	36.9	20.6
29.7	29.8	25.3
23.9	30.6	23.9
28.2	18.5	30.7
30.2	29.2	27.7
30.1	34.5	15.1

Procedure of Analysis

• Arrange and enter the data according to the scheme mentioned above in text file or Excel sheet.
• Enter/paste the data into the text area and press the Submit button.
• Enter the required parameters:
  • Total number of variables in the data file
  • Number of treatments (if using genotypic, phenotypic, or environmental correlations)
  • Observations per variable (for un-replicated data)
  • Dependent variable number (the column corresponding to the dependent variable)
  • Independent variable numbers (list of independent variables separated by spaces)
• Choose the Path Analysis option.
• Select the desired statistics options.
• Press the Analyze button to perform the analysis.