Research Methodology - Dr. Krishan K. Pandey

340 Research Methodology
We may illustrate the path analysis technique in connection with a simple problem of testing a
causal model with three explicit variables as shown in the following path diagram:
Fig. 13.3
The structural equation for the above can be written as:
L
M
NM
X
X
X
1
2
3
O
P
QP
=
=
=
L
M
NM
e1
p21 X1+ e2
p X + p X + e
31 2 32 2 3
O
P
QP
= pX + e
where the X variables are measured as deviations from their respective means. p 21 may be estimated
from the simple regression of X 2 on X 1 i.e., X 2 = b 21 X l and p 31 and p 32 may be estimated from the
regression of X 3 on X 2 and X 1 as under:
X$ = b X + b X
3 312 . 1 21 . 2
where b 31.2 means the standardized partial regression coefficient for predicting variable 3 from
variable 1 when the effect of variable 2 is held constant.
In path analysis the beta coefficient indicates the direct effect of X j (j = 1, 2, 3, ..., p) on the
dependent variable. Squaring the direct effect yields the proportion of the variance in the dependent
variable Y which is due to each of the p number of independent variables X j (i = 1, 2, 3, ..., p). After
calculating the direct effect, one may then obtain a summary measure of the total indirect effect of
X j on the dependent variable Y by subtracting from the zero correlation coefficient r yxj , the beta
coefficient b j i.e.,
Indirect effect of X j on Y = c jy = r yxj – b j
for all j = 1, 2, ..., p.
Such indirect effects include the unanalysed effects and spurious relationships due to antecedent
variables.
In the end, it may again be emphasised that the main virtue of path analysis lies in making explicit
the assumptions underlying the causal connections and in elucidating the indirect effects due to
antecedent variables of the given system.
CONCLUSION
Path Diagram (with the variables)
X 1
p 31
p 21
X 3
From the brief account of multivariate techniques presented above, we may conclude that such
techniques are important for they make it possible to encompass all the data from an investigation in
one analysis. They in fact result in a clearer and better account of the research effort than do the
piecemeal analyses of portions of data. These techniques yield more realistic probability statements
p 32
X 2