**2. Variables and path diagram in health and medicine**

### **2.1 Causality**

SEM models assume probabilistic causality. This allows changes in the results to occur with a probability between 0 and 1.0. The estimation of effects using the data is founded on probability distribution assumptions; thus, causality is understood as a functional relationship between two quantitative variables, effects change a probability distribution. Causality assumptions for a researcher in Medicine and Health are done through a synthesis of logic, theory, and prior knowledge, in this way the causal relationship between observed and latent variables is conceptually hypothesized with expert clinical judgment [2].

The SEM includes observed or manifest variables, latent variables, errors or disturbances, and parameters. There are two main ways to communicate and understand the equations that the SEM represents: through simultaneous equations or by a path diagram. A path diagram is a visualization of the conceptual model, and a conceptual model is an idea of the relationship under study. Behind the ideas of causal inference are Bayesian networks and causal graphs; for example, a causal directed graph can include, common causes, whether measured or unmeasured variables.

#### **2.2 Observed, latent variables, disturbances, and effects**

Observed variables are measured and recorded in the data (e.g. sex, age, height, weight, systolic blood pressure, diastolic blood pressure, body mass index). In a path diagram, these variables are represented by rectangles or a box. A standardized variable is a variable that has a mean zero and a variance one. Latent variables or latent constructs are variables that are not directly measured (e.g. depression, metabolic syndrome, obesity, and anxiety). In a path diagram, they are described by circles or ovals. Observed or latent variables can be exogenous or endogenous. Exogenous variables are variables that are not influenced (not caused) by others variables in a model. This variable is the cause or effect of one or more variables in the model. Endogenous variables are those variables that are influenced by other variables. An endogenous variable can affect another variable of the same type.

### *The Basics of Structural Equations in Medicine and Health Sciences DOI: http://dx.doi.org/10.5772/intechopen.104957*

Disturbances are the unspecified causes of the effect variable. Each endogenous variable is assigned a disturbance, and this is considered as a latent variable.

Effects can be direct, indirect, and totals. These effects can be represented by directed lines. The direct effect (!) is the causal effect of an independent variable on another called dependent, that is, the direct influence of one variable on another. Any variable can be strictly independent (exogenous) or a dependent variable or endogenous.

Indirect effect is a causal effect of an independent variable on a dependent through the pathway of a third variable. This effect is synonymous with the mediation effect. The total effect is the sum of all possible effects of one independent variable on another dependent. All the effects are estimated by various techniques from the sample data.

#### **2.3 Path diagram**

It is a graphical description of an SEM that includes a measurement model and a structural model, where measured or observed variables are represented by rectangles, latent variables by circles, and curved lines represent unanalyzed associations. The covariances or correlations between exogenous variables are described by a curved line with two arrowheads. The variance is represented by two-headed curved arrows on the same variable observed or latent. Here, the latent variables are treated as continuous in what we shall refer to as conventional SEM (or what is sometimes called first-generation SEM). Hypothesized causal effects or direct effects, on endogenous variables, are represented by a line with a single arrowhead.

Kline [1] on parameters of SEM, when means are not included, suggests defining parameters in words that are parallel to three symbols utilized in Reticular Action Model (RAM) symbolis a direct effect, on endogenous variables, is represented by a line with a single arrowhead; double-headed curved arrows that go out and re-enter the same variable, represent the variance of an exogenous variable; and the doubleheaded curved arrows entering one variable and leaving another variable to represent the covariance.

In medicine and health sciences, it is common to assess a latent variable by several observed variables, for example, obesity can be indirectly measured by the observed variables percentage of fat (FAT), body mass index (BMI), and abdominal circumference (AC) (**Figure 1**).

#### **Figure 1.**

*A path diagram representing the latent variable obesity measured by three observed variables: Percentage of FAT (FAT), body mass index (BMI), and abdominal circumference (AC).*
