Week 10 Exercises: Structural Equation Modelling (SEM)

Exercising Exercises

Dataset: tpb2

The “Theory of Planned Behaviour” is a theory about why people engage in certain behaviours. It has been applied in many contexts, and here we are testing the theory as a model of why people exercise.

The theory is represented in the diagram in Figure 1 (only the latent variables and not the measured items are shown). Attitudes refer to the extent to which a person has a favourable view of exercising; subjective norms refer to whether they believe others whose opinions they care about believe exercise to be a good thing; and perceived behavioural control refers to the extent to which they believe exercising is under their control. Intentions refer to whether a person intends to exercise and behaviour is a measure of the extent to which they exercised. Each construct is measured using four items apart from intentions which has five.

Figure 1: Theory of planned behaviour (latent variables only)

The data are available either:

Table 1: Data Dictionary for TPB data
variable question
SN1 When I think about people whose opinions matter to me, I believe they value and support regular exercise
SN2 I feel pressure from those I care about to exercise regularly
SN3 Most people who are important to me approve of my exercising
SN4 Most people like me exercise regularly
PBC1 My exercise routine is up to me and only me
PBC2 I am confident that if I want to then I can exercise regularly
PBC3 I believe I have the ability to overcome any obstacles that may prevent me from exercising regularly.
PBC4 I feel capable of sticking to a consistent exercise schedule, even when faced with challenges or distractions
attitude1 I see exercising as an enjoyable and rewarding activity.
attitude2 I believe that exercising contributes positively to my overall well-being and health.
attitude3 I view exercising as an important part of maintaining a healthy lifestyle.
attitude4 I feel energized and invigorated after engaging in physical exercise.
int1 I am determined to take concrete steps towards establishing a consistent exercise habit
int2 I intend to exercise for at least 20 minutes, three times per week for the next three months.
int3 I have made a firm decision to prioritize exercise and allocate time for it in my schedule
int4 I intend to be in shape within the next three months.
int5 I am committed to incorporating regular exercise into my weekly routine.
beh1 I currently engage in physical activity for at least 20 minutes, three times per week, as recommended.
beh2 I already allocate time for exercise in my weekly schedule and adhere to it regularly.
beh3 I track my exercise sessions and ensure I meet my weekly goals
beh4 I do not currently exercise enough
Question 1

Load in the various packages you will probably need (tidyverse, lavaan), and read in the data using the appropriate function.

We’ve given you .csv files for a long time now, but it’s good to be prepared to encounter all sorts of weird filetypes. Can you successfully read in from both types of data?

Question 2

Before we test the theory of planned behaviour, we want to think about the measurement models for each of the constructs we are trying to capture.

Test separate one-factor models for each construct.
Are the measurement models satisfactory? (check their fit measures).

This isn’t anything new - this is just back to cfa()! So all the same as in the CFA reading, only we need to do it 5 times over..

Question 3

Using lavaan syntax, specify the full structural equation model that corresponds to the model in Figure 1. For each construct use the measurement models from the previous question.

Estimate and evaluate the model

  • Does the model fit well?
  • Are the hypothesised paths significant?

This involves specifying the measurement models for all the latent variables, and then also specifying the relationships between those latent variables. All in the same model!

Question 4

Examine the modification indices and expected parameter changes - are there any additional parameters you would consider including?

Question 5

Test the indirect effect of attitudes, subjective norms, and perceived behavioural control on behaviour via intentions.

Remember, when you fit the model with sem(), use se='bootstrap' to get boostrapped standard errors (it may take a few minutes). When you inspect the model using summary(), get the 95% confidence intervals for parameters with ci = TRUE.

Question 6

Write up your analysis as if you were presenting the work in academic paper, with brief separate ‘Method’ and ‘Results’ sections

Models of pro-environmental behaviour

Warning: ambiguity incoming!!

In some fields, theories are built on top of immutable laws and well defined measures of physical quantities. In much of the behavioural and social sciences, theories can feel a bit more like a “free-for-all”, working with broad, overlapping concepts that are hard to define, let alone measure. It’s not bad, just very difficult!

This next set of exercises are loosely inspired by Kaiser et al., 2006 :Contrasting the Theory of Planned Behavior With the Value-Belief-Norm Model in Explaining Conservation Behavior, and provide an example of how confusing it is to work in this sort of area.

Dataset: consvmodels.csv

The “theory of planned behaviour” (TPB) is a broad psycho-social theory of ‘why people do things’, that you can find applied in all sorts of contexts, from health psychology to business/organisation psychology, to environmental psychology. Broadly speaking, the theory suggests that we do things because they are beneficial, socially acceptable, and do-able.

A contrasting theory, specifically for why people take pro-environmental actions, suggests that we do things because our values inform an ‘environmental worldview’ (a set of beliefs about the state of the world), and this in turn results in taking more pro-environmental actions because it encourages us to consider the consequences of our actions and thus our responsibility and our “Personal Norms” (i.e., our personal moral obligation toward the environment). This theory — the “Value-Belief-Norm (VBN) theory” — contrasts with the TPB idea in that it views behavior as a moral response rather than a rational choice. Essentially, the TPB suggests a decision is made by asking ‘is this action good for me and my social standing?’, where the VBN equivalent question would be ‘is this action the right thing to do based on my duty to the planet?’

We’re going to compare these two theories in terms of how well they predict pro-environmental actions.

We have data from 500 people, all of whom filled out a questionnaire that contained 48 items, measuring each of the constructs involved in both TBP and VBN.

TPB constructs

  • Attitudes - 5 items: att1, att2, att3, att4, att5
  • Pro-environmental Social Norms - 5 items: sn1, sn2, sn3, sn4, sn5
  • Perceived Behavioural Control - 5 items: pbc1, pbc2, pbc3, pbc4, pbc5
  • Pro-environmental Intentions - 5 items: int1, int2, int3, int4, int5

VBN constructs

  • Environmental Worldview (‘New Ecological Paradigm’ questions) - 5 items: nep1, nep2, nep3, nep4, nep5
  • Awareness of Consequences - 5 items: awar1, awar2, awar3, awar4, awar5
  • Environmental Responsibility - 5 items: resp1, resp2, resp3, resp4, resp5
  • Personal Norms - 5 items: pn1, pn2, pn3, pn4, pn5

Outcome (for both TPB and VBN)

  • Conservationist Behaviours - 8 items: cb1, cb2, cb3, cb4, cb5, cb6, cb7, cb8

The data can be found at https://uoepsy.github.io/data/consvmodels.csv

Table 3: Data Dictionary: consvmodels.csv
variable wording
att1 Protecting the environment is beneficial and advantageous for society.
att2 Taking action to help the environment feels satisfying and rewarding to me.
att3 I believe acting in an environmentally friendly way is a sensible and effective thing to do.
att4 Environmental conservation is a wise and productive use of my time.
att5 Overall, I have a highly positive and favorable view of being 'green'.
sn1 I feel social pressure to be more environmentally conscious in my daily life.
sn2 People expect each other to protect the environment.
sn3 People whose opinions I value would approve of people making 'green' choices.
sn4 Many people I look up to take active steps to help the environment.
sn5 Most people who are important to me think I should act environmentally friendly.
pbc1 I am confident that I can perform pro-environmental behaviors if I want to.
pbc2 I have the resources and opportunities I need to protect the environment.
pbc3 For me, living an environmentally friendly lifestyle is easy.
pbc4 Whether or not I act environmentally friendly is entirely up to me.
pbc5 I have complete control over how much I contribute to environmental protection.
int1 I intend to take action to protect the environment in the next month.
int2 I plan to reduce my environmental footprint significantly.
int3 I will make a conscious effort to engage in pro-environmental behaviors.
int4 I am determined to choose 'green' alternatives whenever possible.
int5 I expect to increase my level of environmental conservation in the near future.
nep1 The balance of nature is very delicate and easily upset by human activities.
nep2 Humans are severely abusing the environment.
nep3 Plants and animals have as much right as humans to exist.
nep4 The earth is like a spaceship with very limited room and resources.
nep5 Humans must live in harmony with nature in order to survive.
awar1 If we don't act now, the damage to our ecosystem will be irreversible.
awar2 Climate change will have dangerous consequences for my health and safety.
awar3 I believe that environmental problems have a direct impact on my community.
awar4 Environmental protection will help ensure a better life for future generations.
awar5 Environmental pollution is a major threat to all living things on Earth.
resp1 I feel personally responsible for the environmental problems caused by my lifestyle.
resp2 My individual actions can make a meaningful difference in the environment.
resp3 Every person is responsible for the protection of the natural world.
resp4 I believe I have a duty to help solve the environmental issues we face today.
resp5 I feel a sense of ownership over the environmental impact of my household.
pn1 Protecting the environment is a duty I owe to society and/or the planet.
pn2 I would feel guilty and at fault if I did not take action to help the environment.
pn3 I believe acting in an environmentally friendly way is a morally right and necessary thing to do.
pn4 My conscience would bother me if I ignored environmental issues.
pn5 Overall, I feel that being 'green' is a core requirement of my personal values.
cb1 Consumer Choice: I chose to buy products with less packaging or products made from recycled materials.
cb2 Waste Management: I made a conscious effort to sort and recycle my household waste (paper, plastic, glass).
cb3 Resource Conservation: I reduced my water consumption by taking shorter showers or turning off the tap while brushing teeth.
cb4 Sustainable Shopping: I brought my own reusable bags or containers when shopping to avoid using plastic bags.
cb5 Energy Efficiency: I turned off lights and electronic devices in rooms that were not being used to save electricity.
cb6 Transportation: I opted for public transport, cycling, or walking instead of driving a private car for short trips.
cb7 Chemical Reduction: I used eco-friendly cleaning products or avoided using harsh chemicals in my home/garden.
cb8 Temperature Control: I kept the heating/cooling in my home at a lower/higher setting than usual to save energy.
Question 7

Read in the data. It’s all nice and cleaned and ready to go.

Get some quick plots of item distributions to check things look normal, and get a nice table of descriptive stats for all the variables - stuff like skew and kurtosis.

the functions (both from the psych package) like multi.hist() and describe() are designed for exactly this purpose - quick explorations of lots and lots of variables.

Question 8

In order to compare how well these two theories predict the pro-environmental behaviour, we’re going to want to specify and fit two models, one for the TPB and the other for the VBN theory, but with the same outcome.

Note that in our diagram, that last bit of the two models is the same, going from Intentions->Behaviours.

Before you get started with modelling, check your measurement models for the different constructs, and make any modifications that you deem to be justifiable in order to achieve good fit.

It’s a pain having to write these all out, so if you want to save time you can copy-paste these:

Attitudes =~ att1 + att2 + att3 + att4 + att5

SNorms =~ sn1 + sn2 + sn3 + sn4 + sn5

PBControl =~ pbc1 + pbc2 + pbc3 + pbc4 + pbc5

Intentions =~ int1 + int2 + int3 + int4 + int5

EWV =~ nep1 + nep2 + nep3 + nep4 + nep5

Aware =~ awar1 + awar2 + awar3 + awar4 + awar5

Resp =~ resp1 + resp2 + resp3 + resp4 + resp5

PNorms =~ pn1 + pn2 + pn3 + pn4 + pn5

Conserv_Beh =~ cb1 + cb2 + cb3 + cb4 + cb5 + cb6 + cb7 + cb8

Question 9

Okay, let’s now move to specifying and fitting models that reflect our two theories - TPB and VBN. Do they fit well? are all of the hypothesised paths are significant?

Question 10

Our question is about how well these two theories predict conservationist behaviours.

We’re using the same outcome - conservationist behaviours - so what we would like to know is how much variance in the outcome is explained in each of our models.

We can do that!

inspect(model, what = "rsquare")

Which theory explains more variability in how people engage in pro-environmental behaviours?

Question 11

Let’s take stock of where we are now. We’ve got two competing theories about why people act in environmentally friendly ways. Both theories provide overall good fit to the data. They explain a similar amount of variance in our final outcome measure of conservationist behaviours, but the TPB provides a better prediction of peoples intentions.

To do some more thorough work, we might want to think a bit more about how exactly these two theories differ. If we take a step back a bit, both of these theories are just saying “Something–>Intentions–>Actions”, and they differ in terms of what they say explains why people have different intentions. TPB says our intentions are driven by 3 things (Attitudes, Social Pressure, and amount of control we think we have over our actions), and VBN says they are driven by a chain of things that results in a Personal sense of moral obligation (“Personal Norms”).

So one way we could start to think about assessing these theories, is to ask if the addition of the “Personal Norms” part of VBN provides explanatory power beyond the other parts of the TPB, i.e.:

Fit the model presented in the diagram above. What do you conclude (if anything?)