Outline

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Outline

• 1) Objectives
• 2) Model representation
• 3) Assumptions
• 4) Data type requirement
• 5) Steps for solving problem
• 6) A hypothetical example

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Main readings

• 1) Pedhazur, E. (1997), Multiple regression in
  behavioral research, Third edition, Harcourt
  Brace College Publisher, USA.
• 2) Dillon, W.R. Goldstein, M. (1984),
  Multivariate Analysis Methods and Applications,
  John Wiley Sons, USA.

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Objectives

• 1) Study the direct and indirect effect of
  variables, where some variables are viewed as
  causes of other variables which are viewed as
  effects.
• 2) to shed light on the tenability of the causal
  model a researcher formula based on knowledge and
  theoretical consideration.

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Model representation (1)
A
C
B

• Exogenous variables variables that only acts as
  a predictor or cause for the other variable (e.g.
  A)
• Endogenous variables variables that predicted
  or caused by other variables (e.g. B and C)
• Causal relationship the cause-and-effect
  relationship along each path from a variable to
  other variable, sometimes, the effect will be
  mediated by the third variable(s)

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Model representation (2)

• Each endogenous variable will be represented by
  an equation consisting of the variables on which
  it is hypothesized to be cause and a residual
  representing variables not included in the model.
  
• For example
• A eA
• B pBAAeB
• C pCAApCBBeC

where, pBA path coefficient between
variable A and variable B eB residual of
variable B
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Assumptions

• 1) Relations among variables are linear.
• 2) All error terms (i.e., residuals) are assumed
  to be uncorrelated with each other.
• 3) Only recursive models are considered that is,
  there are only one-way causal flows in the
  system reciprocal causation between variables is
  prohibited.
• 4) The variables are measured without error.

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Data type requirement

• 1) The endogenous variables should be measured
  on an interval scale.
• 2) The exogenous variables could be represented
  as metric or nonmetric data.

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Steps for solving problem

• 1) Develop a theoretically based model
• 2) Construct a path diagram to represent the
  causal model
• 3) Assess the overall model fit
• 4) Estimate the effect for each causal
  relationship

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Steps (1) for solving problem
Developing a theoretically based model

• - the path (causal) model should be justified by
  a theory
• because as Dillon and Goldstein stated
  that cause and
• effect relationships are derived from
  theory, and theory
• comes from outside of statistics.
• - Hair et al. (1997) suggested that theory
  may be based on
• ideas generated from
• 1) priori empirical research
• 2) past experiences and observations of
  actual behavior,
• attitudes, or other phenomena
• 3) other theories in literature

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Example

• Igbaria, M., Zinatelli, N., Cragg, P. and
  Cavaye, A. L. M. (1997), Personal Computing
  Acceptance Factors in Small Firms A Structural
  Equation Model, MIS Quarterly,
• 21(3 ), 279-305.
• Objectives of the study
• 1) to develop a model of the determinants of
• personal computing acceptance
• 2) to examine both the direct and indirect
  effects
• of these determinants of acceptance

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Step (2) for solving problem
Construct a path diagram to represent the causal
model
Internal computing support
Perceived Ease of Use
Internal computing training
Management support
System Usage
External computing support
Perceived Usefulness
External computing training
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Step (2) for solving problem
Construct a path diagram to represent the causal
model
Each endogenous variable will be represented by a
equation consisting of the variables on which it
is hypothesized to be cause and a residual
representing variables not included in the
model. The example included 3 endogenous
variables, therefore, we can generate 3 equation
to represent their causal relationship. The
simplest method to evaluate a causal model is
using multiple regression analysis (MR). As
suggested by Pedhazur (1997) mutliple regression
analysis can be viewed as a special case of path
analysis, it is not surprising to adopt MR for
solving path analysis.

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Step (3) for solving problem
Assess the overall model fit

1) R2 measure of the proportion of the variance
of the in the endogenous constructs which can be
accounted for by its causes (may be the exogenous
or endogenous variables)
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Step (3) for solving problem
Estimate the effect for each causal relationship
1) Path coefficient - the direct effect of a
variable taken as a cause of a variable
taken as an effect - pij the direct effect of
variable j on variable i - if a model is
recursive, the variables are expressed in
standard scores and the assumptions are
reasonably met, path coefficient turn out
to be standardized regression coefficient
obtained in multiple regression analysis.

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Step (3) for solving problem
Estimate the effect for each causal relationship
2) Decomposing correlation - path analysis
allows us to use the simple correlation between
variables to estimate the effects of each causal
relationship in a causal model - a correlation
can be decomposable into four components a)
direct effects b) indirect effects c) spurious
effects d) unanalyzed effects

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Step (3) for solving problem
Estimate the effect for each causal relationship
Indirect effect - the situation where a cause
variable affects an effect variable through a
third variable, which itself directly or
indirectly affects the effect variable For
example Internal computing support affects
system usage through perceived ease of use.

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Step (3) for solving problem
Estimate the effect for each causal relationship
Spurious effect - pertain to the effects of
common antecedent variables on the correlation
between two endogenous variables. - variable C
and D share two common causes, A and B.

A
C
D
B
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Step (3) for solving problem
Estimate the effect for each causal relationship
Unanalyzed effect - pertain a components that
arise from the correlation between exogenous
variables - the correlation between variable C
and A is affected by B, since A and B are
correlated.

A
C
D
B
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Step (3) for solving problem
Estimate the effect for each causal relationship
Total effect is simply the sum of direct and
indirect effect. Most of time, researchers are
only interested in the direct, indirect and total
effect of a causal relationship. Calculation of
the effects a) direct effect path coefficient
standardized regression coefficient b) indirect
effect product the path coefficients along an
indirect route from cause variable to effect
variable via tracing arrows in the headed
direction only c) total effect direct effect
indirect effect

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Step (3) for solving problem
Result

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A hypothetical example
Problem Suppose we are going to study the
factors affecting user satisfaction on using
Intranet. Concluded from extensive literature
review, we hypothesized that perceived ease of
use and perceived usefulness are the two factors
having direct effect on user satisfaction on
using Intranet. We also proposed that the factors
of system quality, information quality and
services quality would influence user
satisfaction indirectly through their effects on
perceived ease of use and perceived usefulness. A
graphical representation on the proposed model is
displayed in Figure 1.

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A hypothetical example

System Quality
Perceived Ease of Use
Information Quality
User Satisfaction
Perceived Usefulness
Services Quality
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A hypothetical example

• - Exogenous variables
• System quality, Information quality, Services
  quality
• - Endogenous variables
• Perceived ease of use, Perceived usefulness,
  User satisfaction
• - Estimate the effects of the causal model
  involves two stages
• 1) all endogenous variables will be regressed on
  their
• cause variables to assess their direct
  effect
• 2) estimate the indirect and total effect

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A hypothetical example
1st round
Table 1 prediction of perceived ease of use and
perceived usefulness

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A hypothetical example
1st round
Table 2 Prediction of user satisfaction on using
Intranet

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A hypothetical example
2nd round removing the insignificant path
Table 1 prediction of perceived ease of use and
perceived usefulness

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A hypothetical example
2nd round removing the insignificant path
Table 2 Prediction of user satisfaction on using
Intranet

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A hypothetical example
Conclusion

• 1) The amount of variance explained by the
  exogenous variables in perceived ease of use and
  perceived usefulness are 27 and 28
  respectively.
• 2) The model as a whole explained 47 of the
  variance in user satisfaction with using
  Intranet.
• 3) System support plays a very important role in
  the studied model because
• a) it has the strongest direct effect on
  perceived ease of use
• (0.328, p?0.05).

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A hypothetical example
Conclusion

• b) it has the strongest direct effect on
  perceived usefulness
• (0.524, p?0.05)
• c) it has the strongest direct effect on user
  satisfaction with
• using Intranet (0.360, p?0.05).
• d) it has the strongest total effect on user
  satisfaction with
• using Intranet.

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