The study was based in the southern part of Kenya, mainly in Kajiado County. The county borders Kiambu and Nakuru counties to the north, Narok County to the west, and Machakos and Makueni counties to the northeast and east, respectively. To the southeast lies Taita Taveta County, while Tanzania forms the southern boundary. Geographically, the county spans approximately 21,871.1 square kilometers, positioned between latitudes 1˚0’S and 3˚0’S and longitudes 36˚5’E and 37˚5’E [12] . The geographical scope of the study, limited to three wards within Kajiado Central Sub-County, is illustrated in Figure 1 . According to the 2019 census, the number of households in the Kajiado Central sub-county was 37,059, with a total land area of 4239 square kilometers and a density of 38 persons per square kilometer [19] . Livestock farming in the sub-county mainly consists of cattle, sheep, and goats. The trade of these animals and their products, such as beef, milk, goat meat (chevon), sheep meat (mutton), along with hides and skins, serves as a vital source of household earnings, enhances dietary needs, and generates employment for local residents [20] .

The study employed a multi-stage sampling approach to collect data from livestock-keeping households in the target sub-county. Initial selection focused on Kajiado County due to its status as the region most significantly affected by Ipomoea plant invasions nationwide. Subsequently, Kajiado Central Sub-County was chosen as the study area as it experiences the highest infestation levels within the county. From this sub-county, three wards (Purko, Dalalekutuk, and Illdamat) were selected. The study employed [21] sample size formula to determine the minimum required sample size, which is the best formula for determining sample size when the variable of interest is a proportion, which is the percentage of households willing to contribute. The study assumed a degree of variability of 0.5, a confidence level of 95%, and a 6% level of precision, as a 6% margin provides a slightly relaxed precision level while ensuring reliable results, making it a practical balance between accuracy and resource constraints.

$n=\frac{Z^{2}pq}{e^2}$ (1)

where: n- Sample rural households required

Z² is the desired confidence interval.

e- is the margin of error

p- is the estimated proportion of households who are willing to pay

q- the proportion of households who are not willing to pay

Therefore, the sample size for this study was $n=\frac{{\left(1.96\right)}^{2}0.5\left(1-0.5\right)}{{\left(0.06\right)}^2}$ n = 266.777 $\approx$ 267.

This research employed a mixed-methods approach for data collection. Primary data, which formed the basis for both descriptive and empirical analysis, were gathered through semi-structured questionnaires administered to selected households in Kajiado Central Sub-County. To complement the findings, secondary data were obtained from diverse sources, including agricultural offices at the sub-county level, national population census records, peer-reviewed journal articles, and book chapters. The survey questionnaire designed for this research aimed to collect data on various household characteristics and, additionally, it included a contingent valuation scenario in the form of a double-bounded dichotomous choice elicitation method with an open-ended follow-up question, which overcomes the complexity associated with questionnaire design and implementation [22] - [24] . While some risk of hypothetical bias remains, this study employed a double-bounded dichotomous choice design to mitigate it. The follow-up question prompts households to think more critically and ground their willingness to pay in a realistic financial context, which helps reduce overstatements and refine the valuation estimates.

Prior to the full-scale data collection, the questionnaire underwent a pilot test involving 22 randomly chosen households across two wards—Matapato North and Matapato South to ensure its validity and clarity [25] . Following the pilot testing phase, the starting bid values were established based on the median willingness-to-pay derived from open-ended responses. The initial bid values (t¹) were set at 4,500, 8,000, 10,000, and 12,000 Kenyan shillings (KES) per household per year, based on the methodologies outlined by [26] - [28] . The follow-up bids (t²) were adjusted dynamically based on the household’s response to the first bid (t¹). If a household accepted the initial bid, the follow-up bid was increased to determine their maximum willingness to pay [26] [29] . These four predetermined bid values were then distributed uniformly and randomly among all surveyed households. The households were assured that the cash annual contribution would be collected efficiently through a mandatory surcharge on existing household utility bills. These collected funds would then be administered by a dedicated and publicly audited trust to ensure they are used solely for the intended conservation purpose.

This study used the Contingent Valuation Method (CVM), which is the most commonly used approach for estimating values that cannot be derived through traditional market mechanisms. A primary reason for its application is its unique capacity to capture both use and non-use values. This methodology has been effectively employed in several recent studies across East Africa, including research by [30] [31] in Ethiopia, [32] in Kenya, and [33] in Uganda, to assess willingness-to-pay for a variety of environmental goods. When analyzing two dichotomous response variables (WTP1 and WTP2), standard probit or logit models prove inadequate for simultaneous equation estimation. In such cases, the seemingly unrelated bivariate probit model emerges as the preferred econometric approach, as it can concurrently estimate both the initial and follow-up bid equations. Assuming the error terms are normally distributed with a mean of zero and variance of δ₁ and δ₂, the WTP₁ and WTP₂ have a bivariate normal distribution with means μ₁ and μ₂ and variances δ₁ and δ₂, and with correlation coefficient ρ, which is the covariance between errors of the two bids. The probability that $WTP₁<t₁$ and $WTP₂<t₂$ i.e.

Pro (No-No) is

$pro\left(u₁+e₁<t₁,u₂+e₂<t₂\right)=\Phi e₁e₂\left(\frac{t₁-u₁}{\delta ₁},\frac{t₂-u₂}{\delta ₂},\rho \right)$ (2)

Pro (No- Yes) is

$pro\left(u₁+e₁<t₁,u₂+e₂\ge t₂\right)=\Phi e₁e₂\left(\frac{t₁-u₁}{\delta ₁},\frac{t₂-u₂}{\delta ₂},\rho \right)$ (3)

Pro (Yes –No) is

$pro\left(u₁+e₁>t₁,u₂+e₂<t₂\right)=\Phi e₁e₂\left(\frac{t₁-u₁}{\delta ₁},\frac{t₂-u₂}{\delta ₂},\rho \right)$ (4)

Pro (Yes- Yes) is

$pro\left(u₁+e₁\ge t₁,u₂+e₂\ge t₂\right)=\Phi e₁e₂\left(\frac{t₁-u₁}{\delta ₁},\frac{t₂-u₂}{\delta ₂},\rho \right)$ (5)

where:

Φ_e1e2 is the standard bivariate normal cumulative distribution function with zero mean and unit variance and correlation coefficient ρ.

${\text{y}}_{1i}=1$ if the response to the first question is yes and 0 otherwise,

${\text{y}}_{2i}=1$ if the response to the second question is yes, and 0 otherwise

${\text{d}}_1{}_i=2y_1{}_i-1$ and ${\text{d}}_2{}_i=2y_2{}_i-1$, i^th contribution to the bivariate probit likelihood function becomes

$L_i\left(u_{₁}/t\right)=\Phi e_{₁}{e}_{₂}[d_{₁i}\left(\frac{{\text{t}}_{₁}-{\text{u}}_{₁}}{{\text{δ}}_{₁}},d_{₂i}\frac{{\text{t}}_{₂}-{\text{u}}_{₂}}{{\text{δ}}_{₂}},d_{₁i}{d}_{₂i}\rho \right)$ (6)

Following [34] , a SUBP model can be specified as follows:

$y_1*={\alpha }_1+{\beta }_1{t}_1+e_1$ (7)

$y_2*={\alpha }_2+{\beta }_2{t}_2+e_2$ (8)

$E\left(e₁|t₁,t₂\right)=E\left(e₂|t₁,t₂\right)=0$ (9)

$Var\left(e₁|t₁,t₂\right)=Var\left(e₂|t₁,t₂\right)=1$ (10)

$Cov\left(e₁,e₂|t₁,t₂\right)=\rho$ (11)

where:

$y₁*$ $is\text{ith respondents' unobservable true WTP at the time of the first bid}$

$WTP₁=1$, if $y^1>Bid₁$, 0 otherwise and $WTP₂=1$, $if{y}^2>Bid₂$, 0 otherwise

$y₂*$ is the i^th respondent’s implicit underlying point estimate at the time of the second Bid

t₁ and t₂ are the 1^st and 2^nd bids offered to the respondents, respectively.

b₁ and b₂ are coefficients of the 1^st and 2^nd bid offered.

e₁ and e₂ are error terms of the 1^st and 2^nd questions.

Finally, the mean willingness to pay from the SUBP model can be calculated using the double-bounded parameter estimation formula specified by [26] .

$MWTP=-\alpha /\beta$ (12)

where: $\alpha$: is a coefficient for the constant term, and

$\beta$: - is a coefficient of the bid offered to the respondent.

The SUBP model is specified with only the bid and a constant term in the equation to achieve two primary objectives: (1) to derive a robust, mean willingness-to-pay (WTP) estimate, calculated as $-\alpha /\beta$, that is generalizable for policy analysis, and (2) to ensure an unbiased estimate of the correlation parameter, which captures the effect of unobserved individual-specific factors that jointly influence both contingent valuation decisions. This parsimonious specification prioritizes the scope and interpretability of the welfare measure over statistical efficiency, accepting that, while the inclusion of socio-economic covariates could improve estimator precision, it would condition WTP estimates on specific sample characteristics, limiting their broader applicability.

When the dependent variable in a regression model is binary, the analysis could be conducted using linear probability, logit, or probit models. However, the results of the linear probability model may generate predicted values less than zero or greater than one, which violates the basic principles of probability. However, logit or probit models generate predicted values between 0 and 1, and they fit well with the non-linear relationship between the probabilities and the explanatory variables [35] . Besides, the probit model works better for bivariate models than the logit model. Furthermore, the double-bounded dichotomous choice question in the current study will have two binary dependent variables. Two latent variables emerged from the two binary dependent variables in this instance. Therefore, in this study, the Seemingly Unrelated Bivariate probit model was used to determine the factors that affect a household’s WTP for the control of Ipomoea plant species [36] . The Seemingly Unrelated Bivariate probit model is specified as follows: -

$Y₁*={\beta }_1{x}_i+{\epsilon }_i$ (13)

$Y_2*={\beta }_2{x}_i+{\epsilon }_i$ (14)

Y = 1 if $Y_i*>I_i*$ (15)

$Y=0$ if $Y_i*<I_i*$ (16)

Where: ß’ = vector of unknown parameters of the model,

Xi = vector of explanatory variables,

Y_i* = unobservable households’ actual WTP for control of Ipomoea plant species,

Yi = discrete response of the respondents for the WTP,

I_i* = the offered initial bid assigned arbitrarily to the i^th respondent,

ԑi = unobservable random component distributed N (0, σ).

The descriptive statistics summarize the demographic, socioeconomic, and institutional characteristics of the surveyed households based on their willingness to pay for the control of the Ipomoea plant species. The mean age of household heads who were willing to pay was 50.51 years, while for those not willing to contribute, the mean age was 41.92 years. The mean monthly income for the willing group was 19,857 Kenyan Shillings, compared to 11,724 Kenyan Shillings for the non-willing group. In terms of education levels, the average number of years of schooling for those who were willing to pay was 5.21 years, while for those not willing it was 3.37 years. The mean household size, measured in adult equivalent ratio (AE), was 5.28 for those willing to pay and 6.05 for those not willing. The average livestock ownership, measured in Tropical Livestock Units (TLU), was 9.56 for the willing household heads and 6.14 for the non-willing. The dependency ratio, calculated based on household members under 15 and over 65 years of age, was 1.21 for the willing households and 1.52 for the non-willing households. Regarding land ownership, the average land size for households willing to pay was 36.97 acres, while for the non-willing households, it was 21 acres. Finally, the past awareness score related to the Ipomoea plant species was 19.22 for willing households and 22.80 for those who were not willing ( Table 1 ). As the t-test result depicts, there was a significant proportion difference in willingness to pay between dependency ratio, past awareness about Ipomoea, family size, livestock ownership, and education level of the household at a 5% probability level, and there was a significant difference between age of the household and willingness to pay at a 1% probability level ( Table 1 ).

*** shows significant variables at the 1% probability level, ** shows significant variables at the 5% probability level, and * shows significance at the 10% probability level.

The descriptive statistics for categorical variables show the distribution of willingness to pay among different household characteristics. In terms of gender, among male household heads, 119 (86.86%) were willing to contribute while 18 (13.14%) were not willing. Among female household heads, 92 (74.80%) were willing to pay, and 31 (25%) were not willing. Regarding land tenure security, willingness to contribute increased with land tenure security, ranging from very insecure (72.73%) to very secure (100%) as outlined in Table 2 . Concerning extension service access, of those who reported having access, 30 (90.91%) were willing and 3 (9.09%) were not willing to contribute. Among those who did not have access, 181 (79.73%) were willing and 46 (20.27%) were not willing. In terms of major livelihood activity, households’ willingness to pay varied from casual laborers (71.43%) to livestock rearing (92.00%) as outlined in Table 2 . Regarding credit access, among households who reported having access to credit, 28 (96.55%) were willing and 1 (3.45%) was not. Among those without access, 183 (79.22%) were willing and 48 (20.78%) were not ( Table 2 ). As the chi-square (χ²) result depicts, there was a significant proportion difference between willingness to pay and major livelihood activities and land security at the 1% probability level, and there was a significant proportion difference between gender and willingness to pay at the 5% probability level ( Table 2 ).

*** shows significant variables at the 1% probability level, ** shows significant variables at the 5% probability level, and * shows significance at the 10% probability level.

A double-bounded dichotomous choice contingent valuation survey result indicated that 30.38% of households accepted both bids, 23.85% accepted the initial bid but rejected the subsequent bid, 26.92% rejected the first bid but accepted the second, and 18.85% rejected both bids ( Figure 2 ).

The empirical estimation of willingness-to-pay (WTP) from the contingent valuation survey aimed to determine the mean WTP distribution, supported by strong statistical evidence. The highly significant Wald chi-square statistic (Wald χ² (2) = 105.56, p < 0.01) ( Table 3 ) confirmed the joint significance of the model’s coefficients, while the Likelihood Ratio test (χ² (1) = 17.03, p < 0.01) validated the interdependence between initial and follow-up responses in the double-bounded dichotomous choice approach. A positive and significant correlation coefficient (ρ = 0.626) indicated related but imperfectly correlated WTP responses, justifying the use of the seemingly unrelated bivariate probit model to account for this dependence while allowing for residual variation. This methodological approach aligns with previous studies by [31] [40] [41] [42] in addressing correlated errors in contingent valuation studies. Based on the parameter estimates and applying [26] formula, the mean annual WTP for proposed Ipomoea control measures was estimated at KES 9,541.44 per household ( Table 3 ). A sensitivity test was conducted to assess the impact of exclusion of protest zeros on mean WTP. When protest zeros were included in the dataset, the mean WTP was estimated at 9,387.29 KES per household. After excluding protest responses, the mean WTP increased to 9,541.44 KES per household. This demonstrates that the treatment of protest responses has a substantial effect on welfare estimates, and thus the primary analysis proceeds with the cleaned dataset excluding protest bids.

Out of the 211 households willing to contribute cash, the majority (94.8%) stated that they needed more pasture for their livestock, highlighting the serious impact Ipomoea has had on forage availability. Additionally, 55.5% believed the proposed control measure was worth the money. This is consistent with the findings of [41] , who found that households were willing to pay for soil conservation of communal lands due to the reason that it was worth the money, and 8.5% expressed a strong interest in managing communal grazing land ( Table 4 ).

In addition to the households who expressed willingness to pay, the study also examined the reasons given by those who rejected the offered bids for the hypothetical intervention to control Ipomoea. 90.74% of households reported they could not afford to pay. This is consistent with the findings of [40] [41] [43] , who identified low financial capacity as a reason and a genuine response. In this study, it was also accepted as a genuine economic limitation. However, five other households rejected the offer on grounds such as that the government should fund the intervention 3 (5.56%) or that it was not their responsibility 2 (3.70%) ( Table 5 ). These five cases were also categorized as protest zeros, as they reflect a rejection of the payment scenario rather than a lack of means.

Before conducting econometric analysis, multicollinearity was checked. Variance Inflation Factors (VIF) and pairwise correlation (pw corr) tests were used for continuous variables and dummy variables, respectively. Based on [35] , multicollinearity is present if VIF is greater than 10. The analysis showed that there was no significant multicollinearity among the dummy variables (Gender, Extension access, Major livelihood activities, and land security). Therefore, all 12 of the predictors that were hypothesized were used in the estimation of the Seemingly Unrelated Bivariate Probit (SUBP) model ( Table 6 ).

The bivariate probit model used in this study was statistically significant overall, confirming the model’s suitability in examining factors influencing households’ willingness to pay for the control of the invasive Ipomoea plant species. In the cash-based willingness to pay model, the Wald chi-square tests for joint significance yielded highly significant results (p-value = 0.0000), indicating that the explanatory variables, taken together, contribute meaningfully to explaining the probability of willingness to pay. Moreover, the rho (ρ) values were significantly different from zero, as evidenced by the Wald test of rho = 0. Specifically, the rho value was 0.406 (p = 0.0351) ( Table 7 ), suggesting that the two equations in the model (e.g., WTP1 and WTP2) are not independent. This validates the use of the bivariate probit model over separate univariate probit models, as it accounts for potential correlation between the unobserved factors influencing the two willingness-to-pay outcomes. In other words, households’ responses to different bid versions are likely interrelated, and modeling them jointly improves estimation efficiency and accuracy. The log pseudo-likelihood values of −267.6 (cash WTP) also indicate good model fit, especially in the context of the Contingent Valuation Method (CVM). Furthermore, the predicted joint probabilities (Pr (WTP1 = 1, WTP2 = 1)) were 0.40 ( Table 7 ), suggesting that a substantial portion of respondents were willing to support Ipomoea control under at least one contribution format.

*** shows significant variables at the 1% probability level, ** shows significant variables at the 5% probability level, and * shows significance at the 10% probability level.

As expected, Initial and Follow-up bid had a negative and statistically significant effect on household willingness to pay for controlling the invasive Ipomoea plant species. In the SUBP model, both Bid1 and Bid2 coefficients were negative and highly significant at the 1% level, indicating that as the proposed monetary contribution increased, households were less likely to accept the bid. Specifically, the joint marginal effects show that a one-unit increase in the bid amount decreased the probability of willingness to pay by approximately 0.0038% to 0.0070%, holding all other variables constant ( Table 7 ). This outcome aligns with the law of demand, which suggests that as the cost of a good or service increases, the likelihood of purchase or support tends to decrease. In this context, increasing the financial contribution required from households reduced their probability of supporting the Ipomoea control initiative. Moreover, this result aligns with previous contingent valuation studies, such as [31] [43] , who also reported a significant negative relationship between bid amount and willingness to pay for environmental services.

As hypothesized, access to extension services had a positive and statistically significant effect on households’ willingness to pay for the control of the invasive Ipomoea plant species. Households with access to extension services were 18.4 percentage points more likely to be willing to pay for the control program at the 5% level in the WTP1 equation compared to those without extension access ( Table 7 ). This implies that households who have received agricultural extension services are better informed and more aware of the negative impacts of Ipomoea on their land, livestock, and livelihoods. The results align with previous research by [42] [44] [45] , which demonstrated that access to extension or advisory services significantly increases community participation in conservation efforts and the management of invasive species.

A household’s primary source of income significantly impacts their willingness to pay for controlling the Ipomoea plant species. As expected, a household’s major livelihood activity had a positive and significant influence on their willingness to pay for Ipomoea control. In the area studied, major livelihood activities are mainly livestock keeping. The marginal effects suggest that a change in the major source of livelihood leads to an approximate 5.7 percentage point increase in the likelihood of a household being willing to pay for Ipomoea control, assuming all other factors remain constant ( Table 7 ). This study result is consistent with the hypothesis and a previous study by [46] , which reported that pastoralists whose only source of livelihood is livestock production are more willing to pay than those who have other alternatives as their primary source of livelihood, such as farming.

The results show that Livestock Ownership (TLU) had a positive and significant influence on the willingness to pay for ipomoea plant species control measures. Households with more livestock units (TLU) were significantly more willing to pay for ipomoea plant species than households with fewer livestock units (TLU). This is expected, as Ipomoea has toxic effects on livestock, and livestock keepers may be more affected by the economic losses caused by the invasive plant. Therefore, an increase in Tropical Livestock Unit by one more increases the households’ WTP by almost 1%, and it happened to be significant at the 5% and 10% probability levels for the first and second responses, respectively, citrus paribus ( Table 7 ). The results are consistent with the findings of [41] [47] [48] , who argued that having a higher TLU indicates not directly households’ intention to rehabilitate the area but rather also indicates their intention to get more fodder both directly from their share and by purchasing from others who do not own at all or own a small herd size, or it is due to economies of scale [49] [50] .

Conversely, household size (Adult Equivalents) had a negative and statistically significant effect on willingness to pay. A one-unit increase in adult-equivalent size reduced the probability of agreeing to pay by about 4.1 percentage points ( Table 7 ). This may be due to larger families facing tighter household budgets or prioritizing other pressing needs over environmental management. The study result is consistent with the findings of [43] [51] , who argued that an increase in family size means more expenditures on other things and decreases the per capita income of the members and hence will decrease participation in environmental or natural resource management. Their reason extends to the fact that an increase in family size decreases the per capita income of the members and, hence, will decrease the payment for environmental goods.