# 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.

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