What does this analysis do?

Structural equation modeling, usually called SEM, allows researchers to examine a network of relationships among several variables at the same time. It draws heavily on regression, but it goes beyond the familiar question of whether one variable predicts another. SEM typically has more than one IV and DV, and allows researchers test a larger explanation of how several variables may be connected.

Explaining SEM with a police investigation board

One way to understand the relationship between latent and observed variables is to think about a crime board from your favorite procedural police show. The board below was created using ChatGPT and demonstrates what it might look like for police investigators who need to establish whether or not a car crash was an accident, and what the motive might be to demonstrate that the car crash was on purpose.

Neither motive nor intent is something an investigator can directly see or measure. Investigators have to gather concrete evidence that helps them evaluate those abstract ideas. Text messages may provide evidence of motive. Information from the vehicle's black box or meteorological reports on the weather the day of the accident may help investigators decide whether the crash was intentional or accidental.

In this situation, the observed variables, like weather data and text messages, allow a police officer to understand latent variables like motive and whether or not the crash was an accident.

To compare this with SEM and the pervious intelligence example:

Intelligence

Crime investigation element

SEM element

What they have in common

Intelligence

Motive or whether the crash was intentional

Latent variable

The big-picture idea we want to understand, even though we cannot directly observe it.

IQ test, class performance

Text messages, witness testimony, black-box data, and road conditions

Observed variable

The concrete evidence we can collect and use to understand the latent variable.

To keep running with the metaphor, a police investigator would probably feel more confident with several pieces of evidence pointing toward motive: credit card statements showing that someone bought tools used in the crime, text messages, and testimony from an eyewitness. In the same way, several useful observed variables can provide a fuller picture of a latent variable.

What research questions can this analsysis explore?

How does employee loyalty affect an employee's intention to stay at a job?

Latent variables: Loyalty (IV) and intention to stay (DV)

Observed variables that could be used to measure loyalty: 

• Participant responses to survey questions about loyalty.

• Employee's length of service with the company.

• Participants' responses to a survey about their attitude and feelings of loyalty towards their direct supervisor

• Participants' responses to a survey about their attitude and feelings of loyalty towards their co-workers.

Observed variables that correspond to intention to stay: 

• Participants' resposnes to survey questions on whether or not they see themselves in their current poisiton a year from now.

• Ask your participants for the number of other jobs they have applied for in the last year.

• Ask participants to list the number of job search-related behaviors they have engaged in in the last year, including but not limited to a) checking job postings with other employers, b) discussing leaving the current job with friends and family, c) revising their resume. 

How do parents' attitudes about reading affect a child's attitude toward reading

Latent variables: Parents' attitudes (IV) and the child's attitude (DV.

Observed variables that could measure parents' attitudes towards reading: 

• Parent responses to survey questions about reading

• The number of books the parent read in the past year.

• The number of adult books in the home.

Observed variables that correspond to the child's attitude toward reading: 

• Contact the child's school for their score on reading aptitude tests.

• Child score on a  reading-attitudes survey

• Ask the child's teacher for the number of times the child voluntarily reads during free time at school.

How does family support affect military members' mental health during deployment?

Family support and mental health are both latent variables.

Observed variables for family support might include family members' responses to a support survey, their participation in available support groups, and the stability of their local support network.

Observed variables for mental health might include scores on depression and anxiety inventories and a supervisor's assessment of the service member's apparent well-being.

1. 1. A list of disciplines (in psych or out of psych) where this type of analysis is often used.

   2. When possible, scaffold onto Intro Stats knowledge base.

2. Laypersons interpretation.

   1. NEW: Introduce an article that odes the thing:

How do I interpret the results of published research using this analysis?

Schmidt and colleagues (2010) studied how 200 Italian high school students appraised and coped with an important final exam that they needed to pass for their diploma.

The researchers proposed a model connecting students' appraisals of the exams, their emotions, and the coping strategies they used. In other words, they asked whether the ways students thought and felt about an important exam were related to how they coped with it.

Several parts of the model were latent variables. These included three types of emotional reactions to exam stress: Frustration and Powerlessness, Anxiety and Fear, and Positive Emotions. The researchers also examined several types of coping, including suppression, reappraisal, social support, distancing, problem-focused coping, and drug use.

2. 2. How to interpret in-text results of this analysis

   3. How to interpret an in-table results of this analysis

   4. How to interpret a data visualization of this analysis (when appropriate)

   5. Potential article(s) that you would like to pull from in your explanation.

   6. Big picture ideas: What can you take away from this analysis? What are the limitations? How do you think about the research question based on findings?

Interpretting SEM

Interpreting SEM