Cycle tour through multivariate statistics: Part 7 Structured Equation Modeling

For the path analysis, I wish to determine the influences several variables have on tourAwesomeness. Typically, the hypothesis would be formulated before data is collected, but in this case, I’m working with the data I’ve got. My first step was to divide the variables into time order of their effect. I categories variables as:

  • Demographic variables. These are variables that are static at the start and describe the respondent: Age, LocNA, Gender.
  • Before tour variables. These are variables that describe the respondent before the tour: PFitness, PWeight, Panniers, TouringBike.
  • During tour variables. These are variables that describe the respondents during the tour: tourMoney, RideDays, Blog.
  • After tour variables. These are variables that describe the respondent after the tour: tourAwesomeness and DoAgain.

I looked at my variables and the bivariate correlations to see which were related to each other with significant correlations. I drew a line between any each of the variables with significant bivariate correlations. From that diagram, I looked for patterns that made sense given the meaning of the data. I extracted the path diagram:

Structured equation modeling initial path diagram
Structured equation modeling initial path diagram
I defined the order of influence as follows: 1) LocNA, 2) Gender, 3) TouringBike, 4) Panniers, 5) RideDays, 6) tourAwesomeness, and 7) DoAgain. The follow hypothesis are indicated in the path diagram:
  • H1. North American location has a positive effect on RideDays, that is, if you are located in North America you are likely to ride more days per week.
  • H2. Female gender has a positive effect on touring bike, that is, if you are female, you are more likely to ride a touring bike.
  • H3. Touring bike has a positive effect on panniers, that is, if you ride a touring bike you are likely to carry more panniers.
  • H4. Panniers has a positive effect on tourAwesomeness, that is, if you carry more panniers you are more likely to have an awesome tour.
  • H5. Panniers has a negative effect on RideDays, that is, the more panniers you carry, the less days you ride.
  • H6. RideDays has a negative effect on tourAwesomeness, that is, the more days per week you ride the less awesome your tour is.
  • H7. RideDays has a negative effect on DoAgain, that is, the more days per week you ride the less likely you are to do the tour again.
  • H8. TourAwesomeness has a positive effect on DoAgain, that is, the more awesome your tour the more likely you will do the tour again.

I ran the regressions as specified in the analysis algorithm, see summary in table below. At this point I should also test the model for fit; however, SPSS does not do this automatically. For the purposes of this example, I will assume model fit. I updated the path diagram with the results of the analysis.

Structured equation modeling analyzed path diagram
Structured equation modeling analyzed path diagram
I checked the results against the hypothesis to get the following:
  • H1. Significant positive relationship. North American location has a positive effect on RideDays, that is, if you are located in North America you are likely to ride more days per week.
  • H2. Significant negative relationship. Positive relationship implies more females (male = 0, female = 1) ride touring bikes (don’t ride touringbikes = 0, ride touring bikes = 1), so the direction of my hypothesis is incorrect. Male gender has a positive effect on touring bike, that is, if you are male, you are more likely to ride a touring bike.
  • H3. Significant and positive relationship. Touring bike has a positive effect on panniers, that is, if you ride a touring bike you are likely to carry more panniers.
  • H4. Not significant.
  • H5. Significant negative relationship. Panniers has a negative effect on RideDays, that is, the more panniers you carry, the less days you ride.
  • H6. Significant negative relationship. RideDays has a negative effect on tourAwesomeness, that is, the more days per week you ride the less awesome your tour is.
  • H7. Not significant.
  • H8. Significant negative relationship, so the direction of my hypothesis was incorrect. TourAwesomeness has a negative effect on DoAgain, that is, the more awesome your tour the less likely you will do the tour again.

Structured equation modeling analysis results

x Dependent variable Results
7 DoAgain ? tourAwesomeness = -.202, p < .05 ? RideDays = Not significant R2 = .067
DoAgain, H0 ? Panniers = .138, p = .084, so too significant ? TouringBike = Not significant ? Gender = Not significant ? LocNA = Not significant
6 tourAwesomeness ? RideDays = -.401, p < .005 ? Panniers = Not significant R2 = .193
tourAwesomeness, H0 ? TouringBike = Not significant ? Gender = Not significant ? LocNA = Not significant
5 RideDays ? Panniers = -.185, p < .05 ? LocNA = .192, p < .05 R2 = .079
RideDays, H0 ? TouringBike = Not significant ? Gender = Not signfiicant
4 Panniers ? TouringBike = .174, p < .05 R2 = .030
Panniers, H0 ? Gender = Not significant ? LocNA = Not significant
3 TouringBike ? Gender =  -.174, p < .05 R2 = .030
TouringBike, H0 ? LocNA = Not significant
2 Gender Not applicable
Gender, H0 ? LocNA = Not significant

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