*4.3. Irrigation Scheme Attribute Preference Heterogeneity*

The unobserved heterogeneities (Table 3 above) imply the presence of differences in preferences among our respondents. Assuming that the scale heterogeneity is discrete, we estimated scaled-LCM to see whether there are meaningful homogeneous segments within the sample based on their preferences for the attributes. The level of response error variance (or scale) determines the quality of the segmentation and hence the part-worth values estimated for each of these classes [31]. We estimated three sets of six latent class models each to see whether the scale parameter influences the segmentation of the respondents. We first estimated non-SLCM Model1-Model6 class models that are homogeneous with respect to response error. Then, we estimated six LCMs (Model7 to Model12 with two scale classes assumed. Lastly, we estimated six LCMs (Model13 to Model18) with three scale classes assumed (Table 4).

Model 10, Model 4, and Model 15 are the three best-fitting LCM models estimated to see whether there are any discrete segments of preference heterogeneity. Model 10 (two scale segments\*three preference segments) is the best-fitting model based on BIC. Yet, the correct classification rate of Model 10 (87.11%) is the least of the three models. Model 4 (four preference segments and no scale heterogeneity) correctly classified the respondents in 89.74% of the cases. Model 15 has a correct classification rate of 87.52%. As the magnitude (Model 10, scale for class 2 = 0.174; Model 15, scale for class 2 = 0.174, and scale for class3=0) and influence on the segmentation of the response error variance is negligible, we focus on Model 4 to describe the different preference segments of the sample.

The four classes of Model 4 contain farm households with overlapping interests. In fact, the level of interest in the attributes of the hypothetical irrigation schemes was different. Respondents in Class 1 (64.3% of the sample) were highly interested in higher irrigation water frequency (Table 5). They were also interested in water availability in the dry season, slight improvement in the water quality, and sharing water with downstream users. They were, however, disinterested in low water quality and the fee they have to pay for irrigation services. In fact, respondents in all segments were expectedly not interested in paying for the service. Except for water-quality-related attributes, respondents in Class 2 (19.25% of the sample) had a comparable preference map for irrigation scheme attributes with

Class 1, albeit with lower intensity. These farmers were not interested in both low and medium irrigation water quality. They were, however, willing to pay for high-quality (cf. low-quality) irrigation water. They also had a strong interest in sharing the irrigation water with downstream users. This is very different from what we saw in Class 3 and Class 4.


**Table 4.** Latent class models with and without scale heterogeneity.

**Table 5.** Estimated part-worth values for the preference classes.


Note: \* *p* < 0.10, \*\* *p* < 0.05, \*\*\* *p* < 0.01.

Farmers in Class 3 (14.3% of the sample) had a very concentrated preference map. They were highly interested in higher water frequency and high water quality (cf. low quality). They also showed a strong disinterest in low irrigation water quality and sharing water with downstream users. This class of farmers was the only one not willing to share water with farmers in the downstream (Table 5). Their unwillingness was very strong, and it might have resulted in the sample level indifference despite their small proportion. Farmers in Class 4 (only 2.3% of the sample) showed a slight interest in increased watering frequency and high-quality (cf. low-quality) irrigation water and a slight disinterest in payment for irrigation. Farmers in Class 3 and Class 4 appeared to be indifferent in some of the attributes or levels in the choice experiment. We discuss this below in detail.

This analysis revealed that our respondents do have distinct differences in terms of their preference for the irrigation scheme attributes considered. It is therefore important to make note of these differences when designing irrigation schemes to ensure that the interventions are in harmony with the expectations of the farm households and, hence, the sustainability of the irrigation facilities to be developed.

#### *4.4. Irrigation Scheme Attribute Nonattendance*

In this section, we present the results of the latent class analyses for identifying unobserved groups based on attribute nonattendance patterns. We estimated three latent class models gradually to capture the extent to which respondents used heuristics to simplify the choice task. The first LC model (LC Model 1 in Table 6) included full attribute attendance or full compensatory choice, complete non-attendance or pure random choice, and one-attribute non-attendance. Therefore, LC Model 1 is a model with seven classes. The second model (LC Model 2 in Table 6) included full-attendance, full non-attendance, one-attribute non-attendance classes with class membership probability greater than 5% from LC Model 1, and two-attribute non-attendance classes. This model has 13 classes. The third model (LC Model 3 in Table 6) has four classes. The classes are full-attendance, full non-attendance, and two other two-attribute non-attendance classes with a membership size of greater than 5% in LC Model 2.


**Table 6.** Irrigation scheme attribute nonattendance pattern.

Note: the three models are all latent class models with different patterns of restriction on the coefficient of the attributes. The models were estimated using LatentGold 5.1 [42]. NA denotes nonattendance. LL is log likelihood. BIC is Bayesian Information Criterion. AIC is Akaike Information Criterion. Class. err. is classification error indicating the level of misclassification.

The final ANA model showed that 22% of the respondents attended to all attributes (Class 1), and 47.1% of them ignored all attributes (Class 2). Similarly, 23.2% of the respondents ignored the quality of irrigation water and access to water by downstream users (Class 15). Of the farmers, 7.6% also ignored access to water by downstream residents and the annual fee for irrigation water.

The results show that there was a high level of random choice among the respondents. There was also low interest in water sharing with downstream, irrigation water quality and the annual irrigation water user charge. This implies that irrigation development and efficiency interventions must take into account the relative importance of these attributes as perceived by farmers.

This reinforces the observation we made above that there is considerable heterogeneity in preferences among sample farmers. This implies that there is a need for understanding the interests and heterogeneities among target users in identifying and targeting irrigation schemes. It will be difficult to develop a scheme and get it accepted by all farm households in each community or agro-ecology. Our study area was relatively small, albeit with a very heterogeneous landscape and farming system. Yet, the level of heterogeneity in the sample population is a reminder of the limit of the extrapolations we can make and the extent to which our recommendations will be relevant to our target community.
