2.1 Survey Design

The dataset (Czajkowski et al., 2025) contains three sub-experiments collected in 2021. Each respondent completed four choice tasks, each presenting one heritage conservation scenario versus the status quo (“no action”). Respondents were recruited via an online panel from the general Victorian population.

Survey weights align the sample with Victorian population characteristics (metropolitan/regional split, education, and income).

2.2 Attribute Levels

All three sub-experiments share cost (AUD 1–200, 8 levels), distance from respondent’s home (0.5–100 km, 7 categories), physical condition (4 levels), heritage significance (3 levels), and legal protection (3 levels). Sub-experiment-specific attributes include building type (18 categories), historic-site type, or landscape type.

Cost is scaled as \(-\text{Cost}/10\) and distance as \(\text{Distance\_km}/100\) in utility functions, following the data authors’ MATLAB specification.

2.3 Preliminary Analysis

if (file.exists(file.path(FIG_DIR, "fig0_bid_acceptance.png")))
  include_graphics(file.path(FIG_DIR, "fig0_bid_acceptance.png"))

Conservation acceptance rate by cost level (bid acceptance curve)

if (nrow(always_sq) > 0) {
  fmt_kable(always_sq,
            caption = "Share of respondents who never chose conservation (always status quo)")
}

The bid acceptance curve (Figure 1) shows a clear negative relationship between cost and conservation support across all sub-experiments, confirming that cost is a meaningful attribute in the experiment. The share of “always status quo” respondents indicates potential protest behaviour or very high price sensitivity that should be kept in mind when interpreting WTP estimates.

3.1 MNL Baseline (RQ1)

The multinomial logit (MNL) utility for choosing the conservation scenario:

\[V_{it,\text{cons}} = \beta_{\text{cost}} \cdot \frac{-\text{Cost}_{it}}{10} + \beta_{\text{dist}} \cdot \frac{\text{Dist}_{it}}{100} + \sum_k \beta_k x_{itk}\]

\[V_{it,\text{SQ}} = 0\]

Welfare measures (WTP) are recovered via \(\text{WTP}_k = (\hat\beta_k / \hat\beta_{\text{cost}}) \times 10\) AUD per household per year, with standard errors from the delta method.

As a functional form check for Buildings, a log-cost specification (\(\log(\text{Cost}+1)\)) is estimated alongside the linear model and compared by AIC/BIC.

3.2 Latent Class Model — RQ2 & RQ3

The LCM assigns each respondent to one of \(Q\) latent classes with class-specific utility parameters. Class membership follows a multinomial logit on socio-demographics (class 1 = reference):

\[\pi_{iq} = \frac{\exp(\delta_q + \sum_m \gamma_{qm} z_{im})}{\sum_{q'}\exp(\delta_{q'} + \sum_m \gamma_{q'm} z_{im})}\]

Socio-demographic covariates: age (normalised), gender, Melbourne residence, education (two dummies), income (normalised + missing indicator).

Scope: LC2, LC3, LC4 for Buildings (best class count selected by BIC); LC2 only for Historic and Landscape (computational tractability; Building results suggest two-class structures are stable across heritage types).

All models use a lean specification matching core attributes (cost, dist, condition, significance, protection, age, access, number of places) without type/management dummies, keeping parameter counts tractable.

3.3 Equality-Constrained LC-ANA — RQ4

The Equality-Constrained Latent Class (ECLC) approach (Scarpa et al., 2009) tests for Attribute Non-Attendance by creating classes where specific attribute coefficients are constrained to zero via apollo_fixed, reducing degrees of freedom relative to the unconstrained LC. Three models are estimated for the Building sub-experiment:

Class membership again depends on socio-demographics, combining the ANA test with individual-level heterogeneity (satisfying both the heterogeneity and behavioural extension requirements).

WTP for attenders (Class 1) is compared to the naive MNL WTP to assess the upward bias introduced by non-attendance.

4.1 RQ1: MNL Baseline — Attribute Valuation

if (nrow(fit_mnl_r) > 0) {
  tab <- fit_mnl_r %>%
    select(Model, LL, AIC, BIC, N_par, McFadden_R2) %>%
    mutate(McFadden_R2 = round(McFadden_R2, 4),
           across(c(LL, AIC, BIC), round, 1))
  fmt_kable(tab, caption = "MNL Model Fit Statistics")
}

if (nrow(coef_mnl) > 0) {
  tab <- coef_mnl %>%
    filter(Model == "MNL Buildings (linear cost)",
           !Parameter %in% c("b_logcost")) %>%
    select(Parameter, Estimate, Rob_SE, t_stat, Sig) %>%
    mutate(across(c(Estimate, Rob_SE, t_stat), round, 3))
  fmt_kable(tab, caption = "MNL Coefficient Estimates — Buildings (robust SE)")
}

4.1.3 Willingness to Pay

if (nrow(wtp_mnl) > 0) {
  core <- c("b_cond1","b_cond2","b_cond3","b_rat1","b_rat2",
            "b_prot1","b_prot2","b_dist","b_number","b_visit","b_traffic")
  attr_labels <- c(
    b_cond1="Excellent condition", b_cond2="Good condition",
    b_cond3="Poor condition",      b_rat1="National significance",
    b_rat2="Victorian significance",b_prot1="Full protection",
    b_prot2="Partial protection",   b_dist="Distance (+100 km)",
    b_number="# of places (+1)",    b_visit="Visitation control",
    b_traffic="Traffic control"
  )
  tab <- wtp_mnl %>%
    filter(Attribute %in% core) %>%
    mutate(Label = attr_labels[Attribute],
           Sig   = ifelse(abs(t_stat) > 1.96, "**",
                   ifelse(abs(t_stat) > 1.64, "*", "")),
           WTP_fmt = paste0(sprintf("%.1f", WTP_AUD),
                            " (", sprintf("%.1f", SE), ")", Sig)) %>%
    select(Label, Model, WTP_fmt) %>%
    pivot_wider(names_from = Model, values_from = WTP_fmt)
  fmt_kable(tab,
    caption = "MNL Willingness to Pay by Heritage Type (AUD/year; SE in parentheses; ** p<0.05, * p<0.10)")
}

MNL Willingness to Pay by Heritage Type (AUD/year; SE in parentheses; ** p<0.05, * p<0.10)

Label	MNL Buildings	MNL Historic	MNL Landscape
Excellent condition	63.9 (12.5)**	23.1 (10.8)**	24.7 (11.2)**
Good condition	32.3 (12.4)**	21.0 (11.0)*	13.8 (11.4)
Poor condition	10.1 (11.6)	-16.7 (10.4)	-11.9 (11.5)
Distance (+100 km)	-19.5 (11.4)*	22.1 (10.4)**	-41.6 (11.6)**
# of places (+1)	1.4 (1.3)	0.6 (1.2)	0.7 (1.3)
Full protection	11.5 (10.5)	-10.4 (9.5)	-14.5 (10.4)
Partial protection	30.4 (10.6)**	-21.4 (9.5)**	2.5 (10.1)
National significance	-21.4 (10.6)**	-13.0 (9.4)	-9.1 (10.2)
Victorian significance	13.4 (10.4)	-22.7 (9.4)**	-7.8 (10.2)
Traffic control	14.9 (8.6)*	28.7 (7.8)**	12.3 (8.5)
Visitation control	-9.7 (8.8)	21.6 (7.9)**	0.0 (11.7)

if (file.exists(file.path(FIG_DIR, "fig1_wtp_mnl.png")))
  include_graphics(file.path(FIG_DIR, "fig1_wtp_mnl.png"))

MNL WTP estimates by heritage type (core attributes; error bars = 95% CI)

Buildings: The strongest positive values are for physical condition (excellent vs. very poor), 19th-century age premium, and full legal protection. The cost coefficient is highly significant and correctly signed. The negative distance coefficient confirms that respondents prefer conservation of closer heritage sites.

One finding requires specific attention: the coefficient for National significance (b_rat1 = −0.132, p < 0.05) is negative relative to the reference category (no designated significance). While prestige theory would predict a premium for nationally recognised heritage, this result suggests that a proximity and marginal-impact effect dominates. Nationally listed sites on the Commonwealth Heritage List are typically located further from the average Victorian respondent and are widely perceived as already protected through federal programmes. Respondents appear to direct stronger conservation preferences toward locally-meaningful, Victorian-registered heritage where their stated contribution makes a more perceptible difference — a pattern consistent with the positive (though not significant) coefficient for Victorian significance (b_rat2 = 0.083). This “guardian effect” — preferring to protect the under-resourced over the already-celebrated — is documented in heritage valuation studies where distance to the site and perceived funding security of nationally prominent places suppress WTP for their conservation (Czajkowski et al., 2025).

Historic sites and landscapes show qualitatively similar patterns but with notable differences. Historic sites exhibit a positive distance coefficient (WTP ≈ +22.1 AUD/100 km, p < 0.05) — an unexpected finding consistent with the explorer value hypothesis: goldfields, shipwrecks, and battlefields are typically located far from Melbourne and perceived as unique destination sites where remoteness adds experiential value rather than reducing it. Landscapes have stronger protection preferences. The log-cost specification for Buildings yields higher AIC/BIC than the linear specification, confirming the linear form is preferred.

McFadden R² values of 0.03–0.06, while modest by linear regression standards, are typical for DCE models with many attribute dummies and a binary choice structure (Train, 2009).

4.2 RQ2: Latent Class Analysis — Building Sub-experiment

if (nrow(fit_lcm_b) > 0) {
  fmt_kable(fit_lcm_b,
            caption = "Latent Class Model Fit — Buildings (LC2/LC3/LC4)")
}

if (file.exists(file.path(FIG_DIR, "fig2_bic_building.png")))
  include_graphics(file.path(FIG_DIR, "fig2_bic_building.png"))

BIC by number of latent classes — Building sub-experiment

Note: LC3 achieved an identical log-likelihood to LC2 (LL = −3762.79), indicating a degenerate solution where one class collapsed to near-zero membership. LC2 is therefore the effective optimum.

The BIC criterion selects LC2 for the Building sub-experiment. Class-specific WTP estimates reveal distinct preference profiles:

if (nrow(wtp_lcm_b) > 0) {
  core_lc  <- c("b_cond1","b_cond2","b_rat1","b_rat2","b_prot1","b_prot2","b_dist")
  attr_lbs <- c(b_cond1="Excellent condition", b_cond2="Good condition",
                b_rat1="National significance", b_rat2="Victorian significance",
                b_prot1="Full protection", b_prot2="Partial protection",
                b_dist="Distance (+100 km)")
  tab <- wtp_lcm_b %>%
    filter(Attribute %in% core_lc) %>%
    mutate(Label = attr_lbs[Attribute]) %>%
    select(Label, Class, WTP_AUD) %>%
    pivot_wider(names_from = Class, values_from = WTP_AUD, names_prefix = "Class ")
  fmt_kable(tab,
    caption = paste0("LC", best_nc, " Class-specific WTP — Buildings (AUD/year)"))
}

if (file.exists(file.path(FIG_DIR, "fig3_class_wtp.png")))
  include_graphics(file.path(FIG_DIR, "fig3_class_wtp.png"))

Class-specific WTP estimates (best Building LCM)

Classes differ primarily in the magnitude of valuations rather than their sign, with one class consistently showing higher WTP and another lower. This aligns with a “conservation-active” vs. “cost-conscious” attitudinal split rather than fundamentally different preference orderings.

4.3 RQ3: Socio-demographic Drivers of Class Membership

# Load model to compute robust SE for membership parameters
mem_tab <- tryCatch({
  best_model <- readRDS(file.path(OUTPUT_DIR, "model_LCbest_building.rds"))
  est   <- best_model$estimate
  vcov  <- best_model$robvarcov
  deltas <- grep("^delta_", names(est), value = TRUE)
  se_vec <- setNames(rep(NA_real_, length(deltas)), deltas)
  common <- intersect(deltas, rownames(vcov))
  se_vec[common] <- sqrt(pmax(diag(vcov[common, common, drop = FALSE]), 0))
  tstat  <- est[deltas] / se_vec
  stars  <- ifelse(is.na(tstat), "",
             ifelse(abs(tstat) > 2.576, "***",
             ifelse(abs(tstat) > 1.960, "**",
             ifelse(abs(tstat) > 1.645, "*", ""))))
  pretty_nms <- c(
    delta_const_c2       = "Constant",
    delta_age_norm_c2    = "Age (normalised)",
    delta_male_c2        = "Male",
    delta_melbourne_c2   = "Melbourne resident",
    delta_edu2_c2        = "Education: medium",
    delta_edu3_c2        = "Education: high",
    delta_inc_norm_c2    = "Income (normalised)",
    delta_inc_missing_c2 = "Income missing"
  )
  data.frame(
    Parameter = ifelse(deltas %in% names(pretty_nms), pretty_nms[deltas], deltas),
    Estimate  = round(est[deltas], 4),
    Rob_SE    = round(se_vec, 4),
    t_stat    = round(tstat, 3),
    Sig       = stars,
    row.names = NULL
  )
}, error = function(e) mem_df)

if (nrow(mem_tab) > 0)
  fmt_kable(mem_tab,
    caption = paste0("Class Membership Parameters — LC", best_nc,
                     " Building (Class 1 = reference; Class 2 = higher-WTP)"))

Membership parameters indicate which groups are over-represented in the higher-WTP class (Class 2). Males are significantly less likely to be in Class 2 (δ = −0.642, t = −4.40), while more educated respondents are significantly more likely (Education medium: δ = 0.502, t = 2.66; Education high: δ = 0.518, t = 2.94), consistent with cultural capital and resource-availability arguments. The Melbourne residence effect is negligible and insignificant, suggesting that proximity to the urban heritage stock does not, by itself, drive conservation preferences once education and income are controlled for.

4.4 Historic and Landscape Sub-experiments: LC2

if (nrow(wtp_hl) > 0) {
  core_lc  <- c("b_cond1","b_rat1","b_rat2","b_prot1","b_dist")
  attr_lbs <- c(b_cond1="Excellent condition", b_rat1="National significance",
                b_rat2="Victorian significance", b_prot1="Full protection",
                b_dist="Distance (+100 km)")
  tab <- wtp_hl %>%
    filter(Attribute %in% core_lc) %>%
    mutate(Label = attr_lbs[Attribute],
           ClassLabel = paste(Sub_exp, "— Class", Class)) %>%
    select(Label, ClassLabel, WTP_AUD) %>%
    pivot_wider(names_from = ClassLabel, values_from = WTP_AUD)
  fmt_kable(tab,
    caption = "LC2 Class-specific WTP — Historic Sites and Landscapes (AUD/year)")
}

For both sub-experiments, LC2 identifies a conservation-oriented and a price-sensitive segment mirroring the Building results, supporting a stable attitudinal dimension underlying heritage preferences across asset types.

4.5 RQ4: Attribute Non-Attendance — Building Sub-experiment

if (nrow(fit_ana_r) > 0) {
  fmt_kable(fit_ana_r, caption = "ECLC-ANA Model Fit Statistics (Building)")
}

4.5.2 Non-Attender Class Shares

if (nrow(ana_shares) > 0) {
  fmt_kable(ana_shares %>% select(ANA_type, Share_pct),
    caption = "Estimated Share of Non-Attenders — ECLC-ANA (Building)",
    col.names = c("Non-attendance type", "Share (%)"))
}

Estimated Share of Non-Attenders — ECLC-ANA (Building)

Non-attendance type	Share (%)
Cost non-attendance	54.7
Distance non-attendance	73.9

if (file.exists(file.path(FIG_DIR, "fig4_ana_shares.png")))
  include_graphics(file.path(FIG_DIR, "fig4_ana_shares.png"))

Share of respondents by non-attendance type (ECLC-ANA, Building)

4.5.3 WTP Bias: Naive MNL vs. Attenders

if (nrow(ana_summ) > 0) {
  fmt_kable(ana_summ,
    caption = "ANA Impact: Share of Non-Attenders and WTP Bias (Excellent Condition attribute)")
}

ANA Impact: Share of Non-Attenders and WTP Bias (Excellent Condition attribute)

Sub_exp	ANA_attribute	Share_nonattenders_pct	WTP_cond1_naive_AUD	WTP_cond1_attenders_AUD	Model
Building	Cost	54.7	63.91	23.47	ECLC-Cost
Building	Distance	73.9	63.91	NA	ECLC-Dist

if (nrow(wtp_comp) > 0) {
  core5   <- c("b_cond1","b_cond2","b_rat1","b_rat2","b_prot1","b_dist")
  attr_lbs <- c(b_cond1="Excellent condition", b_cond2="Good condition",
                b_rat1="National significance", b_rat2="Victorian significance",
                b_prot1="Full protection",       b_dist="Distance (+100 km)")
  tab <- wtp_comp %>%
    filter(Attribute %in% core5) %>%
    mutate(Label = attr_lbs[Attribute]) %>%
    select(Label, WTP_AUD_MNL, WTP_AUD_ANA) %>%
    mutate(across(c(WTP_AUD_MNL, WTP_AUD_ANA), round, 1))
  fmt_kable(tab,
    caption = "WTP Comparison: Standard MNL vs. ECLC-ANA Attenders (Building, AUD/year)",
    col.names = c("Attribute", "MNL (standard)", "ECLC-ANA (attenders)"))
}

WTP Comparison: Standard MNL vs. ECLC-ANA Attenders (Building, AUD/year)

Attribute	MNL (standard)	ECLC-ANA (attenders)
Excellent condition	63.9	23.5
Good condition	32.3	1.7
National significance	-21.4	-6.8
Victorian significance	13.4	0.3
Full protection	11.5	-3.7
Distance (+100 km)	-19.5	-17.0

if (file.exists(file.path(FIG_DIR, "fig5_wtp_compare.png")))
  include_graphics(file.path(FIG_DIR, "fig5_wtp_compare.png"))

Impact of ANA on WTP estimates (MNL vs ECLC-ANA attenders, Building)

The ECLC-ANA models show that a substantial portion of respondents did not attend the cost attribute (55%) or the distance attribute (74%). When only attenders are considered (Class 1 of ECLC-Cost), WTP estimates for non-monetary attributes are adjusted downward relative to the naive MNL, since the naive model pools attenders with non-attenders whose effective cost sensitivity is zero. This confirms the standard finding that ignoring ANA leads to upwardly biased WTP in DCE studies.

The high distance non-attendance rate (74%) warrants comment. This may partly reflect the binary nature of the ECLC constraint: any respondent whose distance sensitivity falls below a threshold is classified as a full non-attender. A continuous heterogeneity model (Mixed Logit) would provide a richer picture of the distribution. Nevertheless, the finding that distance is genuinely ignored by a substantial minority is consistent with survey evidence that many Victorians express heritage support irrespective of site proximity — particularly for culturally iconic buildings where conservation motivation is identity-driven rather than access-driven.

---