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# Research Analysis and Casual Modeling

**What Is Causal Modeling**

Causal

modeling refers to a class of theoretical and methodological techniques for

examining cause-and-effect relationships, generally with nonexperimental data.

Path analysis, structural equation modelling, covariance structure modeling,

and LISREL modeling have slightly different meanings but often are used

interchangeably with the term causal modelling.

Path analysis usually refers to

a model that contains observed variables rather than latent (unobserved)

variables and is analyzed with multiple regression procedures. The other three

terms generally refer to models with latent variables with multiple empirical

indicators that are analyzed with iterative programs such as LISREL or EQS. w

A

common misconception is that these models can be used to establish causality

with nonexperimental data; however, statistical techniques cannot overcome

restrictions imposed by the study’s design. Nonexperimental data provide weak

evidence of causality regardless of the analysis techniques applied.

## Casual Model

A

causal model is composed of later concepts and the hypothesized relationship!

among those concepts. The researcher constructs this model a priority based on

theoretical or research evidence for the direction and sign of the proposed

effects.

Although the model can be based on the observed correlations in the

sample, this practice is not recommended. Empirically derived models capitalize

on sample variations and often contain paths that are not theoretically

defensible; Findings from empirically constructed models should not be interpreted

without replication in another sample.

Stages of Causal Models

Most

causal models contain two or more stages; they have independent variables, one

or more mediating variables, and the final outcome variables. Because the

mediating variables act as both independent and dependent variables, the terms

exogenous and endogenous are used to describe the latent variables. Exogenous

variables are those whose causes are not represented in the model; the causes

of the endogenous variables are represented in the model.

## Structure of Causal Models

Causal

models contain two different structures. The measurement model includes the

latent variables, their empirical indicators (observed variables), and

associated error variances.

The measurement model is based on the factor

analysis model. A respondent’s position on the latent variables is considered

to cause the observed responses on the empirical indicators, so arrows point

from the latent variable to the empirical indicator.

The part of the indicator

that cannot be explained by the latent variable is the error variance generally

due to measurement.

Purposes of Model

The

structural model specifies the relationships among the latent concepts and is

based on the regression model. Each of the endogenous variables has an

associated explained variance, similar to R in multiple regression. The paths

between latent variables represent hypotheses about the relationship between

the variables.

The multistage nature of causal models allows the researcher to

divide the total effects of one latent variable on another into direct and

indirect effects. Direct effects represent one latent variable’s influence on

another that is not transmitted through a third latent variable.

Indirect

effects are the effects of one latent variable that are transmitted through one

or more mediating latent variables. Each latent variable can have many indirect

effects but only one direct effect on another latent variable.

R ecursive or Non-Recursive Model

Causal

models can be either recursive or non recursive . Recursive models have arrows

that point in the same direction; there are no feedback loops or reciprocal

causation paths. Non recursive models contain one or more feedback loops or

reciprocal causation paths. Feedback loops can exist between latent concepts or

error terms.

Issues In Models

An

important issue for non-recursive models is identification status, Identification

status refers to the amount of information (variances and covariances)

available, compared to the number of parameters that are to be estimated.

If

the amount of information equals the number of parameters to be estimated, the

model is **“just identified.”** If the amount of information exceeds the

number of parameters to be estimated, the model is **“overidentified.”**

In both cases, a unique solution for the parameters can be found. With the use

of standard conventions, recursive models are almost always overidentified.

When the amount of information is less than the number of parameters to be

estimated, the model is **” underidentified “** or

**“unidentified,”** and a unique solution is not possible. Non recursive

models are under identified unless instrumental latent variables (a latent

variable for each path that has a direct effect on one of the two latent

variables in the reciprocal causation relationship but only an indirect effect

on the other latent variable) can be specified.

Causal models can be analyzed

with standard multiple regression procedures or structural equation analysis

programs, such as LISREL or EQS (see **“Structural Equation Modeling”**).

Multiple regression is appropriate when each concept is measured with only one

empirical indicator.

Path coefficients (standardized regression coefficients,

or ẞs) are estimated by regressing each endogenous variable on the variables

that are hypothesized to have a direct effect on it. Fit of the model is

calculated by comparing total possible explained variance for the just

identified model with the total explained variance of the proposed

overidentified model ( Pedhazur , 1982).

## Data Requirements For Path Analysis

Data requirements for path analysis

are the same as those for multiple regression:

(a) interval or near-interval

data for the dependent measure

(b) interval, near-interval, or dummy-, effect,

or orthogonally coded categorical data for the independent measures

(c) 5

to 10 cases per independent variable.

Assumptions of multiple regression

must be met.

Benefits of Model

In

summary, causal modeling techniques provide a way to more fully represent the

complexities of the phenomenon, to test theoretical models specifying causal

flow, and to separate the effects of one variable on another into direct and

indirect effects.

Although causal modeling cannot be used to establish

causality, it provides information on the strength and direction of the

hypothesized effects. Thus, causal modeling enables investigators to explore

the process by which one variable might affect another and to identify possible

points for intervention.