Data

lew_data <- read_sav("Lewandowsky.sav")

# 14 conspiracy items (1–4 scale: strongly disagree to strongly agree)
cy_items <- c(
  "CYNewWorldOrder", "CYSARS", "CYPearlHarbor", "CYAIDS",
  "CYMLK", "CYMoon", "CYJFK", "CY911",
  "CYDiana", "CYOkla", "CYCoke", "CYArea51",
  "CYRoswell", "CYClimChange"
)

cy_labels <- c(
  "New World Order", "SARS", "Pearl Harbor", "AIDS",
  "MLK", "Moon landing", "JFK", "9/11",
  "Diana", "Oklahoma City", "Coca-Cola", "Area 51",
  "Roswell", "Climate change"
)

fa_data <- lew_data %>% select(all_of(cy_items)) %>% na.omit()

Questionnaire items

Item wordings are from Table 1 of Lewandowsky et al. (2012). All items used a 4-point scale from strongly disagree (1) to strongly agree (4).

item_wordings <- tibble::tibble(
  Variable = cy_items,
  Label = cy_labels,
  Item = c(
    "A powerful and secretive group known as the New World Order is planning to eventually rule the world through an autonomous world government that would replace sovereign governments.",
    "SARS (Severe Acute Respiratory Syndrome) was produced under laboratory conditions as a biological weapon.",
    "The U.S. government had foreknowledge about the Japanese attack on Pearl Harbor but allowed the attack to take place so as to be able to enter the Second World War.",
    "U.S. agencies intentionally created the AIDS epidemic and administered it to Black and gay men in the 1970s.",
    "The assassination of Martin Luther King Jr. was the result of an organized conspiracy by U.S. government agencies such as the FBI and CIA.",
    "The Apollo moon landings never happened and were staged in a Hollywood film studio.",
    "The assassination of John F. Kennedy was not committed by the lone gunman Lee Harvey Oswald but was rather a detailed organized conspiracy to kill the president.",
    "The U.S. government allowed the 9/11 attacks to take place so that it would have an excuse to achieve foreign and domestic goals that had been determined prior to the attacks.",
    "Princess Diana's death was not an accident but rather an organized assassination by members of the British royal family who disliked her.",
    "The Oklahoma City bombers Timothy McVeigh and Terry Nichols did not act alone but rather received assistance from neo-Nazi groups.",
    "The Coca-Cola company intentionally changed to an inferior formula with the intent of driving up demand for their classic product, later reintroducing it for their financial gain.",
    "Area 51 in Nevada is a secretive military base that contains hidden alien spacecraft and/or alien bodies.",
    "In July 1947, the U.S. military recovered the wreckage of an alien spacecraft from Roswell, NM, and covered up the fact.",
    "The claim that the climate is changing due to emissions from fossil fuels is a hoax perpetrated by corrupt scientists who want to spend more taxpayer money on climate research."
  )
)

item_wordings %>%
  kable(caption = "Conspiracy belief items (Lewandowsky et al., 2012, Table 1)") %>%
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = TRUE) %>%
  column_spec(3, width = "60%")

Conspiracy belief items (Lewandowsky et al., 2012, Table 1)
Variable	Label	Item
CYNewWorldOrder	New World Order	A powerful and secretive group known as the New World Order is planning to eventually rule the world through an autonomous world government that would replace sovereign governments.
CYSARS	SARS	SARS (Severe Acute Respiratory Syndrome) was produced under laboratory conditions as a biological weapon.
CYPearlHarbor	Pearl Harbor	The U.S. government had foreknowledge about the Japanese attack on Pearl Harbor but allowed the attack to take place so as to be able to enter the Second World War.
CYAIDS	AIDS	U.S. agencies intentionally created the AIDS epidemic and administered it to Black and gay men in the 1970s.
CYMLK	MLK	The assassination of Martin Luther King Jr. was the result of an organized conspiracy by U.S. government agencies such as the FBI and CIA.
CYMoon	Moon landing	The Apollo moon landings never happened and were staged in a Hollywood film studio.
CYJFK	JFK	The assassination of John F. Kennedy was not committed by the lone gunman Lee Harvey Oswald but was rather a detailed organized conspiracy to kill the president.
CY911	9/11	The U.S. government allowed the 9/11 attacks to take place so that it would have an excuse to achieve foreign and domestic goals that had been determined prior to the attacks.
CYDiana	Diana	Princess Diana’s death was not an accident but rather an organized assassination by members of the British royal family who disliked her.
CYOkla	Oklahoma City	The Oklahoma City bombers Timothy McVeigh and Terry Nichols did not act alone but rather received assistance from neo-Nazi groups.
CYCoke	Coca-Cola	The Coca-Cola company intentionally changed to an inferior formula with the intent of driving up demand for their classic product, later reintroducing it for their financial gain.
CYArea51	Area 51	Area 51 in Nevada is a secretive military base that contains hidden alien spacecraft and/or alien bodies.
CYRoswell	Roswell	In July 1947, the U.S. military recovered the wreckage of an alien spacecraft from Roswell, NM, and covered up the fact.
CYClimChange	Climate change	The claim that the climate is changing due to emissions from fossil fuels is a hoax perpetrated by corrupt scientists who want to spend more taxpayer money on climate research.

Response distributions

Most items are heavily skewed toward 1 (disagree). The 1–4 ordinal scale warrants polychoric (latent) correlations.

dist_data <- fa_data %>%
  pivot_longer(everything(), names_to = "item", values_to = "response") %>%
  mutate(item = factor(item, levels = cy_items, labels = cy_labels)) %>%
  group_by(item, response) %>%
  summarise(n = n(), .groups = "drop") %>%
  group_by(item) %>%
  mutate(pct = n / sum(n)) %>%
  ungroup() %>%
  # Order items by mean response (i.e., endorsement)
  left_join(
    fa_data %>%
      pivot_longer(everything(), names_to = "item", values_to = "response") %>%
      mutate(item = factor(item, levels = cy_items, labels = cy_labels)) %>%
      group_by(item) %>%
      summarise(mean_resp = mean(response), .groups = "drop"),
    by = "item"
  ) %>%
  mutate(
    item = fct_reorder(item, mean_resp),
    response = factor(response, levels = 1:4,
      labels = c("Strongly disagree", "Disagree", "Agree", "Strongly agree"))
  )

ggplot(dist_data, aes(x = item, y = pct, fill = response)) +
  geom_bar(stat = "identity") +
  geom_text(
    aes(label = ifelse(pct >= 0.04, paste0(round(pct * 100), "%"), "")),
    position = position_stack(vjust = 0.5), size = 3
  ) +
  coord_flip() +
  scale_y_continuous("Percentage", labels = scales::percent) +
  scale_fill_brewer(palette = "Paired", name = "Response") +
  labs(x = NULL, title = "Response distributions (ordered by mean endorsement)") +
  theme_bw()

GG_save(file.path(figs_dir, "distributions.png"))

Correlation matrix (polychoric)

Because the items are ordinal (4-point scale), we use polychoric correlations to estimate the latent correlations.

poly <- polychoric(fa_data)
R_poly <- poly$rho
colnames(R_poly) <- rownames(R_poly) <- cy_labels

corrplot(
  R_poly,
  method = "color",
  type = "lower",
  addCoef.col = "black",
  number.cex = 0.6,
  tl.cex = 0.8,
  tl.col = "black",
  col = colorRampPalette(c("#2166AC", "white", "#B2182B"))(200),
  title = "Polychoric correlation matrix of conspiracy items",
  mar = c(0, 0, 2, 0)
)

png(file.path(figs_dir, "corrplot.png"), width = 9, height = 9, units = "in", res = 300)
corrplot(
  R_poly, method = "color", type = "lower", addCoef.col = "black",
  number.cex = 0.6, tl.cex = 0.8, tl.col = "black",
  col = colorRampPalette(c("#2166AC", "white", "#B2182B"))(200),
  title = "Polychoric correlation matrix of conspiracy items",
  mar = c(0, 0, 2, 0)
)
invisible(dev.off())

The correlation matrix shows a near-positive manifold: almost all inter-item correlations are positive, suggesting a general conspiracy-belief factor accounts for the bulk of shared variance. However, the magnitudes vary considerably — some items (e.g., Moon landing, AIDS) correlate weakly with others.

Determining the number of factors

fa.parallel(
  R_poly, n.obs = nrow(fa_data), fa = "both", fm = "pa",
  main = "Parallel analysis scree plot (polychoric)"
)

## Parallel analysis suggests that the number of factors =  5  and the number of components =  2

png(file.path(figs_dir, "scree.png"), width = 7, height = 5, units = "in", res = 300)
fa.parallel(R_poly, n.obs = nrow(fa_data), fa = "both", fm = "pa",
  main = "Parallel analysis scree plot (polychoric)")

## Parallel analysis suggests that the number of factors =  5  and the number of components =  2

invisible(dev.off())

The scree plot shows a dominant first eigenvalue with a sharp drop-off, consistent with a strong general factor. The second eigenvalue is near the parallel analysis threshold, making the case for a second factor marginal.

Factor analyses

We compare extraction methods on the polychoric correlation matrix. Both 1-factor and 2-factor solutions are examined, since the scree plot indicates the variance is dominated by a general factor.

print_loadings <- function(fa_obj, title) {
  ld <- as.data.frame(unclass(fa_obj$loadings))
  ld$Item <- cy_labels[match(rownames(ld), cy_items)]
  if (is.null(ld$Item)) ld$Item <- rownames(ld)
  ld$h2 <- fa_obj$communalities
  ld %>%
    select(Item, everything()) %>%
    kable(digits = 3, caption = title) %>%
    kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)
}

eigen_vals <- eigen(R_poly)$values
n_kaiser <- sum(eigen_vals > 1)

1-factor models

PAF — 1 factor

fa_paf_1 <- fa(
  r = R_poly, n.obs = nrow(fa_data),
  nfactors = 1, fm = "pa"
)
print(fa_paf_1, cut = 0.2, sort = TRUE)

## Factor Analysis using method =  pa
## Call: fa(r = R_poly, nfactors = 1, n.obs = nrow(fa_data), fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## AIDS             4 0.87 0.759 0.24   1
## Diana            9 0.82 0.665 0.33   1
## Moon landing     6 0.80 0.638 0.36   1
## 9/11             8 0.79 0.629 0.37   1
## Roswell         13 0.78 0.604 0.40   1
## Area 51         12 0.77 0.588 0.41   1
## SARS             2 0.74 0.554 0.45   1
## MLK              5 0.74 0.548 0.45   1
## JFK              7 0.71 0.507 0.49   1
## New World Order  1 0.69 0.472 0.53   1
## Pearl Harbor     3 0.65 0.425 0.57   1
## Coca-Cola       11 0.61 0.371 0.63   1
## Oklahoma City   10 0.42 0.180 0.82   1
## Climate change  14 0.29 0.086 0.91   1
## 
##                 PA1
## SS loadings    7.03
## Proportion Var 0.50
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## df null model =  91  with the objective function =  10.62 with Chi Square =  12091.13
## df of  the model are 77  and the objective function was  2.95 
## 
## The root mean square of the residuals (RMSR) is  0.09 
## The df corrected root mean square of the residuals is  0.09 
## 
## The harmonic n.obs is  1145 with the empirical chi square  1524.3  with prob <  1.5e-267 
## The total n.obs was  1145  with Likelihood Chi Square =  3356.73  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.677
## RMSEA index =  0.193  and the 90 % confidence intervals are  0.187 0.199
## BIC =  2814.41
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.97
## Multiple R square of scores with factors          0.95
## Minimum correlation of possible factor scores     0.90

print_loadings(fa_paf_1, "PAF — 1 factor")

PAF — 1 factor
	Item	PA1	h2
New World Order	NA	0.687	7.025
SARS	NA	0.744	7.025
Pearl Harbor	NA	0.652	7.025
AIDS	NA	0.871	7.025
MLK	NA	0.741	7.025
Moon landing	NA	0.799	7.025
JFK	NA	0.712	7.025
9/11	NA	0.793	7.025
Diana	NA	0.816	7.025
Oklahoma City	NA	0.424	7.025
Coca-Cola	NA	0.609	7.025
Area 51	NA	0.767	7.025
Roswell	NA	0.777	7.025
Climate change	NA	0.293	7.025

ML — 1 factor

fa_ml_1 <- fa(
  r = R_poly, n.obs = nrow(fa_data),
  nfactors = 1, fm = "ml"
)
print_loadings(fa_ml_1, "ML — 1 factor")

ML — 1 factor
	Item	ML1	h2
New World Order	NA	0.689	0.475
SARS	NA	0.751	0.564
Pearl Harbor	NA	0.652	0.426
AIDS	NA	0.875	0.766
MLK	NA	0.741	0.549
Moon landing	NA	0.814	0.662
JFK	NA	0.687	0.473
9/11	NA	0.794	0.631
Diana	NA	0.812	0.660
Oklahoma City	NA	0.420	0.176
Coca-Cola	NA	0.608	0.369
Area 51	NA	0.761	0.579
Roswell	NA	0.773	0.597
Climate change	NA	0.307	0.094

PCA — 1 component

pca_1 <- principal(
  R_poly, nfactors = 1,
  n.obs = nrow(fa_data)
)
print_loadings(pca_1, "PCA — 1 component")

PCA — 1 component
	Item	PC1
New World Order	NA	0.718
SARS	NA	0.768
Pearl Harbor	NA	0.685
AIDS	NA	0.874
MLK	NA	0.765
Moon landing	NA	0.814
JFK	NA	0.741
9/11	NA	0.809
Diana	NA	0.829
Oklahoma City	NA	0.461
Coca-Cola	NA	0.645
Area 51	NA	0.787
Roswell	NA	0.796
Climate change	NA	0.322

The 1-factor solution is broadly consistent across all three extraction methods. Loadings vary across items — some (e.g., New World Order, SARS, 9/11, Roswell) load moderately, while others (Moon landing, AIDS, Oklahoma City) load weakly, indicating they are poor indicators of a general conspiracy factor.

2-factor models (Kaiser eigenvalue > 1)

PAF — 2 factors (oblimin)

This replicates the original SPSS analysis.

fa_paf_2 <- fa(
  r = R_poly, n.obs = nrow(fa_data),
  nfactors = n_kaiser, rotate = "oblimin",
  fm = "pa", normalize = TRUE
)
print(fa_paf_2, cut = 0.2, sort = TRUE)

## Factor Analysis using method =  pa
## Call: fa(r = R_poly, nfactors = n_kaiser, n.obs = nrow(fa_data), rotate = "oblimin", 
##     fm = "pa", normalize = TRUE)
## Standardized loadings (pattern matrix) based upon correlation matrix
##                 item  PA1   PA2   h2   u2 com
## 9/11               8 0.86       0.71 0.29 1.1
## MLK                5 0.85 -0.26 0.71 0.29 1.2
## AIDS               4 0.81  0.21 0.76 0.24 1.1
## Diana              9 0.78       0.66 0.34 1.0
## JFK                7 0.75       0.54 0.46 1.0
## Moon landing       6 0.71  0.28 0.66 0.34 1.3
## Pearl Harbor       3 0.69       0.46 0.54 1.0
## Roswell           13 0.69  0.27 0.63 0.37 1.3
## SARS               2 0.69       0.56 0.44 1.1
## Area 51           12 0.69  0.26 0.61 0.39 1.3
## Coca-Cola         11 0.60       0.37 0.63 1.0
## New World Order    1 0.55  0.45 0.60 0.40 1.9
## Oklahoma City     10 0.52 -0.26 0.28 0.72 1.5
## Climate change    14       0.73 0.56 0.44 1.0
## 
##                        PA1  PA2
## SS loadings           6.77 1.34
## Proportion Var        0.48 0.10
## Cumulative Var        0.48 0.58
## Proportion Explained  0.83 0.17
## Cumulative Proportion 0.83 1.00
## 
##  With factor correlations of 
##     PA1 PA2
## PA1 1.0 0.2
## PA2 0.2 1.0
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 2 factors are sufficient.
## 
## df null model =  91  with the objective function =  10.62 with Chi Square =  12091.13
## df of  the model are 64  and the objective function was  2.16 
## 
## The root mean square of the residuals (RMSR) is  0.05 
## The df corrected root mean square of the residuals is  0.06 
## 
## The harmonic n.obs is  1145 with the empirical chi square  590.75  with prob <  2.7e-86 
## The total n.obs was  1145  with Likelihood Chi Square =  2453.09  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.717
## RMSEA index =  0.181  and the 90 % confidence intervals are  0.175 0.187
## BIC =  2002.33
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1  PA2
## Correlation of (regression) scores with factors   0.97 0.87
## Multiple R square of scores with factors          0.95 0.75
## Minimum correlation of possible factor scores     0.89 0.50

print_loadings(fa_paf_2, "PAF with oblimin rotation — 2 factors")

PAF with oblimin rotation — 2 factors
	Item	PA1	PA2	h2
New World Order	NA	0.553	0.446	8.119
SARS	NA	0.687	0.183	8.119
Pearl Harbor	NA	0.694	-0.099	8.119
AIDS	NA	0.805	0.212	8.119
MLK	NA	0.853	-0.264	8.119
Moon landing	NA	0.711	0.279	8.119
JFK	NA	0.750	-0.085	8.119
9/11	NA	0.860	-0.155	8.119
Diana	NA	0.785	0.105	8.119
Oklahoma City	NA	0.521	-0.257	8.119
Coca-Cola	NA	0.601	0.035	8.119
Area 51	NA	0.686	0.256	8.119
Roswell	NA	0.694	0.265	8.119
Climate change	NA	0.064	0.734	8.119

ML — 2 factors (oblimin)

fa_ml_2 <- fa(
  r = R_poly, n.obs = nrow(fa_data),
  nfactors = n_kaiser, rotate = "oblimin",
  fm = "ml", normalize = TRUE
)
print_loadings(fa_ml_2, "ML with oblimin rotation — 2 factors")

ML with oblimin rotation — 2 factors
	Item	ML1	ML2	h2
New World Order	NA	0.547	0.169	0.457
SARS	NA	0.638	0.140	0.551
Pearl Harbor	NA	0.736	-0.075	0.470
AIDS	NA	0.885	0.002	0.787
MLK	NA	0.925	-0.185	0.650
Moon landing	NA	0.582	0.283	0.650
JFK	NA	0.573	0.165	0.488
9/11	NA	0.843	-0.025	0.681
Diana	NA	0.679	0.168	0.649
Oklahoma City	NA	0.436	-0.002	0.189
Coca-Cola	NA	0.535	0.093	0.364
Area 51	NA	0.014	0.938	0.899
Roswell	NA	0.040	0.922	0.904
Climate change	NA	0.075	0.255	0.098

PCA — 2 components (oblimin)

pca_2 <- principal(
  R_poly, nfactors = n_kaiser, rotate = "oblimin",
  n.obs = nrow(fa_data)
)
print_loadings(pca_2, "PCA with oblimin rotation — 2 components")

PCA with oblimin rotation — 2 components
	Item	TC1	TC2
New World Order	NA	0.594	0.474
SARS	NA	0.727	0.165
Pearl Harbor	NA	0.732	-0.162
AIDS	NA	0.827	0.189
MLK	NA	0.849	-0.300
Moon landing	NA	0.746	0.267
JFK	NA	0.784	-0.149
9/11	NA	0.863	-0.184
Diana	NA	0.814	0.071
Oklahoma City	NA	0.589	-0.465
Coca-Cola	NA	0.651	-0.010
Area 51	NA	0.727	0.239
Roswell	NA	0.734	0.245
Climate change	NA	0.095	0.852

The 2-factor solution is unstable across extraction methods. The second factor changes identity depending on the method: ML extracts an aliens/space factor (Area 51 and Roswell loading strongly), while PAF extracts a climate factor where only the climate change item loads heavily — a degenerate single-item factor. Items shift between factors depending on the method, and neither second factor is substantively compelling. This instability, combined with the marginal second eigenvalue and the near-positive manifold in the correlation matrix, suggests the 2-factor solution is not robust. The data are better described by a single general factor with varying item quality.

pa_result <- fa.parallel(
  R_poly, n.obs = nrow(fa_data), fa = "fa", fm = "pa",
  plot = FALSE
)

## Parallel analysis suggests that the number of factors =  5  and the number of components =  NA

n_pa <- pa_result$nfact

if (n_pa > n_kaiser) {
  fa_paf_pa <- fa(
    r = R_poly, n.obs = nrow(fa_data),
    nfactors = n_pa, rotate = "oblimin",
    fm = "pa", normalize = TRUE
  )
  print_loadings(fa_paf_pa, paste0("PAF with oblimin rotation (parallel analysis: ", n_pa, " factors)"))
}

PAF with oblimin rotation (parallel analysis: 5 factors)
	Item	PA1	PA3	PA4	PA2	PA5	h2
New World Order	NA	0.319	0.116	0.050	0.479	0.055	9.936
SARS	NA	0.155	0.145	0.390	0.195	0.209	9.936
Pearl Harbor	NA	0.683	0.033	0.009	0.030	-0.063	9.936
AIDS	NA	0.572	0.014	0.167	0.231	0.359	9.936
MLK	NA	0.631	-0.072	0.321	-0.017	-0.056	9.936
Moon landing	NA	0.201	0.319	0.220	0.156	0.332	9.936
JFK	NA	0.367	0.141	0.380	0.211	-0.511	9.936
9/11	NA	0.872	0.126	-0.057	-0.117	0.053	9.936
Diana	NA	0.198	0.198	0.421	0.149	0.146	9.936
Oklahoma City	NA	-0.011	0.033	0.580	-0.098	-0.052	9.936
Coca-Cola	NA	0.126	0.131	0.374	0.082	0.113	9.936
Area 51	NA	-0.009	1.049	-0.063	-0.041	-0.034	9.936
Roswell	NA	-0.029	0.885	0.071	0.030	-0.005	9.936
Climate change	NA	-0.139	0.000	-0.105	1.045	-0.030	9.936

Factor diagrams

fa.diagram(fa_paf_1, main = "PAF — 1 factor", cut = 0.2)

png(file.path(figs_dir, "diagram_1f.png"), width = 8, height = 6, units = "in", res = 300)
fa.diagram(fa_paf_1, main = "PAF — 1 factor", cut = 0.2)
invisible(dev.off())

fa.diagram(fa_paf_2, main = "PAF — 2 factors (oblimin)", cut = 0.2)

png(file.path(figs_dir, "diagram_2f.png"), width = 10, height = 6, units = "in", res = 300)
fa.diagram(fa_paf_2, main = "PAF — 2 factors (oblimin)", cut = 0.2)
invisible(dev.off())

Factor scores and correlations with external variables

We score both the 1-factor and 2-factor PAF solutions and correlate them with the external variables in the dataset: free market ideology, climate science acceptance, other science acceptance, and perceived environmental problem resolution.

Note: this dataset contains no demographic variables (age, gender, education, etc.). The “external” variables are all attitudinal scales from the same survey.

# 1-factor scores
fa_scored_1 <- fa(
  r = fa_data, nfactors = 1,
  fm = "pa", scores = "regression"
)

# 2-factor scores
fa_scored_2 <- fa(
  r = fa_data, nfactors = n_kaiser,
  rotate = "oblimin", fm = "pa",
  normalize = TRUE, scores = "regression"
)

scores_1f <- as.data.frame(fa_scored_1$scores)
names(scores_1f) <- "General_conspiracy"

scores_2f <- as.data.frame(fa_scored_2$scores)
names(scores_2f) <- paste0("Factor", 1:n_kaiser)

# Bind factor scores to the complete-case rows
scored_data <- lew_data %>%
  select(all_of(cy_items)) %>%
  mutate(.row = row_number()) %>%
  na.omit()

full_scored <- lew_data[scored_data$.row, ] %>%
  bind_cols(scores_1f) %>%
  bind_cols(scores_2f)

# Define external variable groups
ext_flat <- c(
  "FreeMarket",
  "FMUnresBest", "FMNotEnvQual", "FMLimitSocial",
  "FMMoreImp", "FMThreatEnv", "FMUnsustain",
  "AcceptClimSci",
  "CO2TempUp", "CO2AtmosUp", "CO2WillNegChange", "CO2HasNegChange",
  "CauseHIV", "CauseSmoke", "CauseCO2",
  "ConsensHIV", "ConsensSmoke", "ConsensCO2",
  "CFCNowOK", "AcidRainNowOK"
)

factor_names <- c("General_conspiracy", paste0("Factor", 1:n_kaiser))
cor_mat <- cor(
  full_scored[, factor_names],
  full_scored[, ext_flat],
  use = "pairwise.complete.obs"
)

as.data.frame(t(round(cor_mat, 3))) %>%
  mutate(Variable = rownames(.)) %>%
  select(Variable, everything()) %>%
  kable(digits = 3, caption = "Correlations: factor scores with external variables") %>%
  kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)

Correlations: factor scores with external variables
	Variable	General_conspiracy	Factor1	Factor2
FreeMarket	FreeMarket	0.036	-0.095	0.256
FMUnresBest	FMUnresBest	0.013	-0.104	0.213
FMNotEnvQual	FMNotEnvQual	0.109	0.097	0.102
FMLimitSocial	FMLimitSocial	0.028	-0.055	0.165
FMMoreImp	FMMoreImp	0.038	-0.067	0.211
FMThreatEnv	FMThreatEnv	0.026	-0.090	0.221
FMUnsustain	FMUnsustain	0.043	-0.071	0.231
AcceptClimSci	AcceptClimSci	-0.157	-0.011	-0.371
CO2TempUp	CO2TempUp	-0.172	-0.039	-0.359
CO2AtmosUp	CO2AtmosUp	-0.171	-0.029	-0.373
CO2WillNegChange	CO2WillNegChange	-0.145	0.000	-0.360
CO2HasNegChange	CO2HasNegChange	-0.107	0.019	-0.301
CauseHIV	CauseHIV	-0.338	-0.266	-0.370
CauseSmoke	CauseSmoke	-0.292	-0.197	-0.379
CauseCO2	CauseCO2	-0.216	-0.063	-0.426
ConsensHIV	ConsensHIV	-0.147	-0.104	-0.185
ConsensSmoke	ConsensSmoke	-0.087	-0.044	-0.141
ConsensCO2	ConsensCO2	-0.199	-0.071	-0.371
CFCNowOK	CFCNowOK	0.050	-0.008	0.133
AcidRainNowOK	AcidRainNowOK	0.047	-0.015	0.138

cor_long <- as.data.frame(t(cor_mat)) %>%
  mutate(Variable = rownames(.)) %>%
  pivot_longer(-Variable, names_to = "Factor", values_to = "r") %>%
  mutate(
    Factor = factor(Factor, levels = factor_names),
    Variable = factor(Variable, levels = rev(ext_flat))
  )

ggplot(cor_long, aes(x = Factor, y = Variable, fill = r)) +
  geom_tile(color = "white") +
  geom_text(aes(label = sprintf("%.2f", r)), size = 3.2) +
  scale_fill_gradient2(
    low = "#2166AC", mid = "white", high = "#B2182B",
    limits = c(-1, 1)
  ) +
  labs(
    title = "Factor score correlations with external variables",
    fill = "r"
  ) +
  theme_minimal() +
  theme(axis.text.y = element_text(size = 9))

GG_save(file.path(figs_dir, "cor_heatmap.png"))

Summary

Items: 14 conspiracy belief items measured on a 1–4 scale, heavily skewed toward disagreement (floor effects throughout).
Polychoric correlations were used because the items are ordinal. The correlation matrix shows a near-positive manifold, consistent with a general conspiracy-belief factor.
The scree plot shows a dominant first eigenvalue; the second is marginal.
1-factor models (PAF, ML, PCA) produce consistent loading patterns. Item quality varies — some items are poor indicators of the general factor.
2-factor models are unstable across extraction methods: PAF and ML yield substantially different loading patterns for the same data, indicating the second factor is not robust.
Factor scores from both solutions were correlated with free market ideology, climate science acceptance, science cause/consensus beliefs, and environmental problem resolution.

Lewandowsky et al. (2012) — Conspiracy Beliefs Factor Analysis

Emil O. W. Kirkegaard (with Claude Opus 4.6, Anthropic)

2026-03-07