A Structural Equation Model (SEM) is a quantitative statistical analysis that examines causal relations between variables or between items. The nature of the relations is determined by theory or research design.
There are two types of SEM models:
1) Measurement Model
A measurement model investigates how certain survey questions (or scale items) tap into the characteristic of interest. For example, in factor analysis researchers test whether certain latent variables, the characteristics being measured, are indicated by the use of certain items. This serves to validate the surveys used to measure the characteristic of interest.
2) Structural Model
Structural models investigate hypothesized causal relations. For example, to test the Rhodes (2005) model that relationships with mentors improve quality of life by influencing relationships with parents, a structural model is tested.
Example from the mentoring literature:
Although the great summary by Laura Yovienne is short and simple, Chan, Rhodes, Howard, Schwartz, Lowe, & Herrera, (2013) tested a very complex SEM model. In the original paper, the authors first test a measurement model to confirm that the variables of interest are indicated by the survey items. This confirms that a question that measured quality of relationship with mentor factors with the other items on this scale more tightly than with another scale (e.g., quality of relationship with teacher).
A theoretical model that quality of relationship influences a variety of academic and social outcomes was tested using a structural SEM model. In their model (Figure 2 in the paper, p. 137), the authors confirm that quality of mentoring relationships influences parental and teacher relationship quality, which lead to higher academic achievement and social conduct.
Structural Equation Modeling can be used to confirm the measurement of characteristics by validating surveys. This is called a measurement model.
SEM can also be used to measure the relations between a number of characteristics. This is called a structural model.
Note, although it is preferable to have at least 150 participants to run SEM, modeling can be accomplished with less participants.
SEM can be fairly easily applied by using statistical packages such as MPlus or Amos.