03 - Construct brand measure
Rui
2025-03-01
file_path <- "/Users/ra/Library/CloudStorage/Box-Box/2024-Summer/Misleading Claims/Data/Brand Equity Survey/02 - processed data/df_brand_long.csv"
df <- read_csv(file_path, show_col_types = FALSE)round(cor(df[,-1]),2)## awareness_1 awareness_2 awareness_3 awareness_4_reversed
## awareness_1 1.00 0.91 0.89 0.64
## awareness_2 0.91 1.00 0.84 0.61
## awareness_3 0.89 0.84 1.00 0.61
## awareness_4_reversed 0.64 0.61 0.61 1.00
## loyalty_1 0.54 0.51 0.58 0.35
## loyalty_2 0.46 0.43 0.47 0.29
## loyalty_3 0.39 0.37 0.41 0.25
## quality_1 0.47 0.47 0.44 0.28
## quality_2 0.44 0.44 0.40 0.25
## loyalty_1 loyalty_2 loyalty_3 quality_1 quality_2
## awareness_1 0.54 0.46 0.39 0.47 0.44
## awareness_2 0.51 0.43 0.37 0.47 0.44
## awareness_3 0.58 0.47 0.41 0.44 0.40
## awareness_4_reversed 0.35 0.29 0.25 0.28 0.25
## loyalty_1 1.00 0.73 0.71 0.38 0.33
## loyalty_2 0.73 1.00 0.71 0.41 0.39
## loyalty_3 0.71 0.71 1.00 0.33 0.29
## quality_1 0.38 0.41 0.33 1.00 0.85
## quality_2 0.33 0.39 0.29 0.85 1.00Total aggregation and partial aggregation
average across people Cronbach’s alpha is good - the 9 items are reliable
# Calculate brand_equity_ta as the sum of all columns except 'brand'
# Calculate brand equity and component metrics
df_brand_equity_long <- df %>%
mutate(
# Overall brand equity (sum of all metrics)
brand_equity_ta = rowSums(select(., -brand)),
# Component averages - grouping related columns
awareness_pa = rowSums(select(., starts_with("awareness"))),
loyalty_pa = rowSums(select(., starts_with("loyalty"))),
quality_pa = rowSums(select(., starts_with("quality")))
) %>%
select(brand, brand_equity_ta, awareness_pa, loyalty_pa, quality_pa)
# Group by brand to get averages if multiple rows per brand
df_brand_equity <- df_brand_equity_long %>%
group_by(brand) %>%
summarize(
avg_brand_equity_ta = mean(brand_equity_ta),
avg_awareness_pa = mean(awareness_pa),
avg_loyalty_pa = mean(loyalty_pa),
avg_quality_pa = mean(quality_pa)
)library(psych)##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alphaalpha_result <- psych::alpha(df[,-1])
print(paste("Cronbach's alpha for brand equity:", round(alpha_result$total$raw_alpha, 3)))## [1] "Cronbach's alpha for brand equity: 0.896"library(lavaan)## Warning: package 'lavaan' was built under R version 4.3.3## This is lavaan 0.6-19
## lavaan is FREE software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2cov## The following object is masked from 'package:tm':
##
## inspectcfa_model <- '
brand_equity =~ awareness_1 + awareness_2 + awareness_3 + awareness_4_reversed +
loyalty_1 + loyalty_2 + loyalty_3 + quality_1 + quality_2
'
configural_model <- cfa(
model = cfa_model,
data = df
)
summary(configural_model, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 30 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 18
##
## Number of observations 1179
##
## Model Test User Model:
##
## Test statistic 2785.546
## Degrees of freedom 27
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8935.053
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.690
## Tucker-Lewis Index (TLI) 0.587
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12905.722
## Loglikelihood unrestricted model (H1) -11512.949
##
## Akaike (AIC) 25847.444
## Bayesian (BIC) 25938.747
## Sample-size adjusted Bayesian (SABIC) 25881.573
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.294
## 90 Percent confidence interval - lower 0.285
## 90 Percent confidence interval - upper 0.304
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.154
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## brand_equity =~
## awareness_1 1.000 1.335 0.964
## awareness_2 1.042 0.016 66.339 0.000 1.391 0.928
## awareness_3 0.911 0.014 63.293 0.000 1.217 0.917
## awrnss_4_rvrsd 0.717 0.025 28.407 0.000 0.957 0.657
## loyalty_1 0.416 0.017 24.563 0.000 0.556 0.598
## loyalty_2 0.376 0.019 19.833 0.000 0.501 0.513
## loyalty_3 0.299 0.018 16.658 0.000 0.399 0.447
## quality_1 0.315 0.016 19.784 0.000 0.421 0.512
## quality_2 0.293 0.016 18.061 0.000 0.391 0.477
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .awareness_1 0.137 0.012 11.850 0.000 0.137 0.071
## .awareness_2 0.313 0.017 18.011 0.000 0.313 0.139
## .awareness_3 0.279 0.015 19.016 0.000 0.279 0.159
## .awrnss_4_rvrsd 1.207 0.051 23.590 0.000 1.207 0.569
## .loyalty_1 0.554 0.023 23.775 0.000 0.554 0.642
## .loyalty_2 0.704 0.029 23.957 0.000 0.704 0.737
## .loyalty_3 0.638 0.027 24.055 0.000 0.638 0.800
## .quality_1 0.498 0.021 23.959 0.000 0.498 0.738
## .quality_2 0.519 0.022 24.014 0.000 0.519 0.772
## brand_equity 1.782 0.079 22.419 0.000 1.000 1.000cfa_model_second_order <- 'Awareness =~ awareness_1 + awareness_2 + awareness_3 + awareness_4_reversed
Loyalty =~ loyalty_1 + loyalty_2 + loyalty_3
Quality =~ quality_1 + quality_2
f4 =~ 1*Awareness + 1*Loyalty + 1*Quality
f4 ~~ f4'
secondorder <- cfa(cfa_model_second_order, data=df)
summary(secondorder,fit.measures=TRUE,standardized=TRUE)## lavaan 0.6-19 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
##
## Number of observations 1179
##
## Model Test User Model:
##
## Test statistic 297.687
## Degrees of freedom 26
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8935.053
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.969
## Tucker-Lewis Index (TLI) 0.958
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11661.792
## Loglikelihood unrestricted model (H1) -11512.949
##
## Akaike (AIC) 23361.584
## Bayesian (BIC) 23457.960
## Sample-size adjusted Bayesian (SABIC) 23397.609
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.094
## 90 Percent confidence interval - lower 0.085
## 90 Percent confidence interval - upper 0.104
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.993
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.128
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Awareness =~
## awareness_1 1.000 1.227 0.968
## awareness_2 1.041 0.017 62.231 0.000 1.277 0.917
## awareness_3 0.905 0.016 57.791 0.000 1.110 0.898
## awrnss_4_rvrsd 0.718 0.027 26.319 0.000 0.881 0.627
## Loyalty =~
## loyalty_1 1.000 0.825 0.870
## loyalty_2 1.029 0.028 36.139 0.000 0.849 0.859
## loyalty_3 0.900 0.026 34.238 0.000 0.742 0.823
## Quality =~
## quality_1 1.000 0.838 0.974
## quality_2 0.897 0.027 33.715 0.000 0.752 0.887
## f4 =~
## Awareness 1.000 0.506 0.506
## Loyalty 1.000 0.752 0.752
## Quality 1.000 0.740 0.740
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## f4 0.385 0.024 16.334 0.000 1.000 1.000
## .awareness_1 0.103 0.012 8.896 0.000 0.103 0.064
## .awareness_2 0.307 0.017 17.649 0.000 0.307 0.158
## .awareness_3 0.294 0.015 19.344 0.000 0.294 0.193
## .awrnss_4_rvrsd 1.199 0.051 23.633 0.000 1.199 0.607
## .loyalty_1 0.218 0.015 14.638 0.000 0.218 0.243
## .loyalty_2 0.256 0.016 15.511 0.000 0.256 0.262
## .loyalty_3 0.263 0.015 17.877 0.000 0.263 0.323
## .quality_1 0.038 0.018 2.160 0.031 0.038 0.051
## .quality_2 0.154 0.015 9.991 0.000 0.154 0.214
## .Awareness 1.120 0.056 20.015 0.000 0.744 0.744
## .Loyalty 0.295 0.027 11.036 0.000 0.434 0.434
## .Quality 0.318 0.027 11.662 0.000 0.453 0.453cfa_model_2 <- 'Awareness =~ awareness_1 + awareness_2 + awareness_3 + awareness_4_reversed
Loyalty =~ loyalty_1 + loyalty_2 + loyalty_3
Quality =~ quality_1 + quality_2 '
cfa_model_2_config <- cfa(cfa_model_2, data=df)
summary(cfa_model_2_config,fit.measures=TRUE,standardized=TRUE)## lavaan 0.6-19 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Number of observations 1179
##
## Model Test User Model:
##
## Test statistic 157.218
## Degrees of freedom 24
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8935.053
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.985
## Tucker-Lewis Index (TLI) 0.978
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11591.558
## Loglikelihood unrestricted model (H1) -11512.949
##
## Akaike (AIC) 23225.116
## Bayesian (BIC) 23331.637
## Sample-size adjusted Bayesian (SABIC) 23264.933
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.069
## 90 Percent confidence interval - lower 0.059
## 90 Percent confidence interval - upper 0.079
## P-value H_0: RMSEA <= 0.050 0.001
## P-value H_0: RMSEA >= 0.080 0.036
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.033
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Awareness =~
## awareness_1 1.000 1.348 0.973
## awareness_2 1.033 0.015 68.953 0.000 1.393 0.929
## awareness_3 0.899 0.014 64.138 0.000 1.211 0.913
## awrnss_4_rvrsd 0.712 0.025 28.799 0.000 0.960 0.659
## Loyalty =~
## loyalty_1 1.000 0.812 0.874
## loyalty_2 1.021 0.029 34.853 0.000 0.829 0.848
## loyalty_3 0.896 0.027 33.209 0.000 0.728 0.815
## Quality =~
## quality_1 1.000 0.791 0.963
## quality_2 0.918 0.030 30.821 0.000 0.726 0.886
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Awareness ~~
## Loyalty 0.639 0.040 15.829 0.000 0.583 0.583
## Quality 0.539 0.036 14.801 0.000 0.505 0.505
## Loyalty ~~
## Quality 0.294 0.023 12.965 0.000 0.458 0.458
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .awareness_1 0.103 0.011 9.066 0.000 0.103 0.053
## .awareness_2 0.309 0.017 17.926 0.000 0.309 0.137
## .awareness_3 0.292 0.015 19.447 0.000 0.292 0.166
## .awrnss_4_rvrsd 1.201 0.051 23.650 0.000 1.201 0.566
## .loyalty_1 0.203 0.014 14.056 0.000 0.203 0.236
## .loyalty_2 0.268 0.017 16.103 0.000 0.268 0.281
## .loyalty_3 0.267 0.015 18.103 0.000 0.267 0.336
## .quality_1 0.049 0.017 2.808 0.005 0.049 0.073
## .quality_2 0.145 0.016 9.159 0.000 0.145 0.215
## Awareness 1.816 0.080 22.815 0.000 1.000 1.000
## Loyalty 0.660 0.037 18.075 0.000 1.000 1.000
## Quality 0.625 0.033 19.124 0.000 1.000 1.000# Extract factor scores for the three latent constructs
set.seed(123)
factor_scores <- lavPredict(cfa_model_2_config)
# Convert to a dataframe
factor_scores_df <- as.data.frame(factor_scores)
# Print first few rows to check
head(factor_scores_df)## Awareness Loyalty Quality
## 1 -0.2145019 0.06555883 -0.4169187
## 2 1.3820715 0.18035722 0.5507155
## 3 2.5623720 0.03916644 1.5063882
## 4 1.6013624 0.23186990 0.7782253
## 5 -0.1801002 0.91625140 -0.3999667
## 6 -1.0252646 -0.82338523 -0.4477277df_brand_factor_score <- cbind(df_brand_equity_long, factor_scores_df)
df_brand_equity_factorscore <- df_brand_factor_score %>%
group_by(brand) %>%
summarize(
avg_awareness_fs = mean(Awareness),
avg_loyalty_fs = mean(Loyalty),
avg_quality_fs = mean(Quality)
)df_merged <- merge(df_brand_equity, df_brand_equity_factorscore, by = "brand")#write.csv(df_merged, "brand_equity_construct.csv")Compare these measure
awareness_cor <- cor(df_merged %>% select(avg_awareness_pa, avg_awareness_fs))
loyalty_cor <- cor(df_merged %>% select(avg_loyalty_pa, avg_loyalty_fs))
quality_cor <- cor(df_merged %>% select(avg_quality_pa, avg_quality_fs))
print(awareness_cor)## avg_awareness_pa avg_awareness_fs
## avg_awareness_pa 1.0000000 0.9977038
## avg_awareness_fs 0.9977038 1.0000000print(loyalty_cor)## avg_loyalty_pa avg_loyalty_fs
## avg_loyalty_pa 1.0000000 0.9922517
## avg_loyalty_fs 0.9922517 1.0000000print(quality_cor)## avg_quality_pa avg_quality_fs
## avg_quality_pa 1.0000000 0.9973586
## avg_quality_fs 0.9973586 1.0000000# Create standardized versions of all measurement variables
df_merged <- df_merged %>%
mutate(
# Standardize the survey scores
z_awareness_pa = scale(avg_awareness_pa),
z_loyalty_pa = scale(avg_loyalty_pa),
z_quality_pa = scale(avg_quality_pa),
# Note: Factor scores are typically already standardized,
# but we can ensure they're on the same scale
z_awareness_fs = scale(avg_awareness_fs),
z_loyalty_fs = scale(avg_loyalty_fs),
z_quality_fs = scale(avg_quality_fs)
)# Reshape data for easier plotting
library(tidyr)
library(ggplot2)
# For awareness comparison
awareness_comparison <- df_merged %>%
select(brand, z_awareness_pa, z_awareness_fs) %>%
pivot_longer(cols = c(z_awareness_pa, z_awareness_fs),
names_to = "measure_type",
values_to = "standardized_value")
# Plot density comparison
ggplot(awareness_comparison, aes(x = standardized_value, fill = measure_type)) +
geom_density(alpha = 0.5) +
labs(title = "Comparison of Awareness Measures",
x = "Standardized Value",
y = "Density") +
theme_minimal()
# You can create similar plots for loyalty and quality# For loyalty comparison
loyalty_comparison <- df_merged %>%
select(brand, z_loyalty_pa, z_loyalty_fs) %>%
pivot_longer(cols = c(z_loyalty_pa, z_loyalty_fs),
names_to = "measure_type",
values_to = "standardized_value")
# Plot density comparison for loyalty
ggplot(loyalty_comparison, aes(x = standardized_value, fill = measure_type)) +
geom_density(alpha = 0.5) +
labs(title = "Comparison of Loyalty Measures",
x = "Standardized Value",
y = "Density") +
theme_minimal()
# For quality comparison
quality_comparison <- df_merged %>%
select(brand, z_quality_pa, z_quality_fs) %>%
pivot_longer(cols = c(z_quality_pa, z_quality_fs),
names_to = "measure_type",
values_to = "standardized_value")
# Plot density comparison for quality
ggplot(quality_comparison, aes(x = standardized_value, fill = measure_type)) +
geom_density(alpha = 0.5) +
labs(title = "Comparison of Quality Measures",
x = "Standardized Value",
y = "Density") +
theme_minimal()