Factor Analysis in R: Measuring Consumer Involvement

Involvement is a marketing metric that describes the relevance of a product or service in somebody's life. Judy Zaichkowsky defines consumer involvement formally as “a person's perceived relevance of the object based on inherent needs, values, and interests”. People who own a car will most likely be highly involved with purchasing and driving the vehicle due to the money involved and the social role it plays in developing their public self. Consumers will most likely have a much lower level of involvement with the instant coffee they drink than with their clothes.

For my dissertation about customer service in water utilities, I measured the level of involvement that consumers have with tap water using the Personal Involvement Index (PII).

Asking consumers directly about their level of involvement would not lead to a stable answer because each respondent will interpret the question differently. The best way to measure psychological states or psychometrics is to ask a series of questions linguistically related to the topic of interest.

The most cited method to measure consumer involvement is the Personal Involvement Index, developed by Judy Zaichowsky. This index is a two-dimensional scale consisting of the following:

• Cognitive involvement (importance, relevance, meaning, value and need)
• Affective involvement (involvement, fascination, appeal, excitement and interest).

The survey instrument consists of ten Semantic Differential items. A Semantic Differential is a rating scale designed to measure the meaning of objects, events or concepts. The researcher translates the concept, such as involvement, into a list of synonyms and their associated antonyms.

In the involvement survey, participants position their views between two extremes, such as Worthless and Valuable or Boring and Interesting. The level of involvement is the sum of all answers, which is between 10 and 70.

The data form part of a survey of tap water customers.

  ## Consumer Involvement
  library(tidyverse)
  library(psych)

  # Clean data
  customers <- read_csv("data/customer_survey.csv")[-1, ] %>%
    type_convert() %>%
    filter(is.na(term)) %>%
    select(c(1, 21:51, -33)) %>% 
    rename(customer_id = 1)

The scale uses reverse polarity as some of the items are from low to high (boring – interesting) and other from high to low (important – unimportant), so we need to correct this by reversing the scores for six items. The data also has missing values, so we only use the complete cases.

# Correct polarity

pii <- select(customers, customer_id, starts_with("p")) %>%
  mutate(p01 = 8 - p01,
         p02 = 8 - p02,
         p07 = 8 - p07,
         p08 = 8 - p08,
         p09 = 8 - p09,
         p10 = 8 - p10)

# Remove missing values

pii <- pii[complete.cases(pii), ]

This data set contains other information, and the code selects only those variable names starting with "p" (for Personal Involvement Inventory). Before we analyse data, we remove customers who provided the same answers to all items or did not respond to all questions. These responses are most likely invalid, which leaves 757 rows of data.

A boxplot is a convenient way to view the responses to multiple survey items in one visualisation. This plot immediately shows an interesting pattern in the answers. Responses to the first five items were generally higher than those for the last five. This result indicates a distinction between cognitive and affective involvement.

  # Visualise PII

  pii %>%
    pivot_longer(-customer_id, names_to = "Item", values_to = "Response") %>%
    ggplot(aes(Item, Response)) +
    geom_boxplot(fill = "#f7941d") +
    theme_bw(base_size = 12) + 
    labs(title = "personal Involvement Index",
         subtitle = paste("Tap Water Consumers USA and Australia (n =",
                          nrow(pii), ")"))

The next step in the exploratory analysis is to investigate how these factors correlate. The correlation plot below shows that all items strongly correlate with each other. Corresponding with the boxplots above, the first five and the last five items correlate more strongly. This plot suggests that the two dimensions of the involvement index correlate. The following section shows how to use factor analysis in R to check the significance of these correlation patterns.

  # Visualise correlation matrix
  c_matrix <- cor(pii[, -1])

  library(ggcorrplot)
  
  ggcorrplot(c_matrix, outline.col = "white") +
    labs(title = "Personal Inventory Index",
         subtitle = "Correlation Matrix")

Researchers often confuse Factor Analysis with Principal Component Analysis. The outcomes are very similar when applied to the same data set. Both methods are similar but have a different purpose. Principal Component Analysis is a data-reduction technique that reduces the number of variables in a problem. The specific purpose of Factor Analysis is to uncover latent variables. The mathematical principles for both methods are similar but not the same and should not be confused.

One of the most crucial decisions in factor analysis is to decide how to rotate the factors. There are two types: orthogonal and oblique. In simple terms, orthogonal rotations reduce the correlation between dimensions, and oblique rotation allows dimensions to relate to each other. Because of the strong correlations in the correlation plot and the fact that both dimensions measure involvement, this analysis uses oblique rotation. The visualisation below shows how each item and the two dimensions relate.

  library(psych)
  pii_fa <- fa(pii[, -1], nfactors = 2, rotate = "oblimin", fm = "ml")
  fa.diagram(pii_fa, main = NULL)

This analysis suggests that the items for the PII measure an underlying construct, which we can call consumer involvement. To work out the scores for this measure, we can sum the items for each respondent.

  # Calculating the PII
  
  pii_scores <- pii %>%
    mutate(cognitive = p01 + p02 + p03 + p04 + p05,
           affective = p06 + p07 + p08 + p09 + p10) %>%
    select(customer_id, cognitive, affective)

  pivot_longer(pii_scores, cols = -customer_id) %>%
    ggplot(aes(value)) +
    geom_histogram(fill = "dodgerblue 4", binwidth = 1) +
    facet_wrap(~name) +
    theme_minimal(base_size = 12) +
    labs(title = "Consumer Involvement with Tap Water",
         subtitle = "Personal Involvement Index")

This simple factor analysis in R shows the basic principle of analysing psychometric data. The psych package has many more specialised tools to dig deeper into the information. This article has not assessed this construct's validity or evaluated the factors' reliability. That may be for a future article.

Chapter 8 in Data Science for Water Utilities explains the principles of analysing survey data to understand the customer experience in more detail.

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