Agriculture and Environment, 4 (1978) 111--121 111 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

A N A P P L I C A T I O N O F D I S C R I M I N A N T A N A L Y S I S F O R T H E E V A L U A T I O N O F T H E L O C A L E N V I R O N M E N T A L I M P A C T O F L I V E S T O C K P R O D U C T I O N

IAN HODGE

Department of AgTicultural Economics, University of Newcastle upon Tyne (Great Britain)

(Received 15 August 1977; revised 13 January 1978)

ABSTRACT

Hodge, I.D., 1978. An application of discriminant analysis for the evaluation of the local environmental impact of livestock production. Agric. Environm., 4: 111--121.

Intensive livestock production can cause serious nuisance to those who live around livestock units. While no method of measuring the extent of such local farm impact exists, it is difficult to make rational decisions concerning the location and control of intensive livestock production. This paper presents a possible approach to the assessment of the impact resulting from livestock production using discriminant analysis. The population living around livestock farms is divided into two groups: those who feel that there is a nuisance, and those who do not. This division is then related to other variables concerning both the location and nature of the individuals, and from these data a linear discriminant function is calculated, which allocates a score to each individual. The score represents the extent to which the individual is in a position to be caused a nuisance, based upon the perceptions of all those included in the survey. The total of the scores of those living around one live- stock unit, adjusted for the population size, can then be used to compare the impact of this unit with others. It would he possible to create a more general function on the basis of a larger number of surveys, and such a function could be used to estimate the potential impact of a unit while it is still at the planning stage. Thus the size of the score could aid decisions regarding the desirability of that unit in that particular location. Similarly, in such situations, the functions could identify potential problems, and plans for the intended livestock unit could be examined for possible ways of reducing the environmental impact.

INTRODUCTION

Changes have t a k e n p lace in t he m e t h o d s and t e c h n o l o g y o f l ives tock p r o d u c t i o n , wh ich have inc reased the e x t e n t o f t he e n v i r o n m e n t a l i m p a c t which can resul t . These changes have ar isen f r o m the e c o n o m i c pressures which are f aced b y p r o d u c e r s and i t seems l ike ly t h a t these pressures will c o n t i n u e to encou rage the g r o w t h in t he scale and i n t e n s i t y o f l ives tock p r o d u c t i o n in t he fu tu re . A wide range o f e x t e r n a l cos ts ( these m a y be d e f i n e d as cos ts resu l t ing f r o m s o m e ac t o f p r o d u c t i o n o r c o n s u m p t i o n , fo r wh ich no m e c h a n i s m exis ts w h e r e b y t h o s e suf fe r ing t h e m rece ive a d e q u a t e c o m p e n - sa t ion t h r o u g h the m a r k e t ) can be caused b y l ives tock p r o d u c t i o n . In th is

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paper, a specific group of these costs are to be considered. These are exper- ienced by those people living around farms with livestock enterprises. The types of external costs which have their effects indirectly, such as the build-up of drugs and chemicals in food products, are excluded. A method of making an evaluation of these costs, which can then be related to other farms causing similar impact using discriminant analysis, is described.

THE NATURE OF LOCAL FARM IMPACT

Local environmental impact may occur in a number of different ways, many of which are of ten regarded as small nuisances but which can in some circumstances cause considerable distress. The most common of these are smell, effluent on roads, insect pests and noise. This type of environmental problem has been discussed by Willinger (1974).

The scale of impact depends upon three major areas: (i) the agricultural conditions; (ii) the ease of passage of the externality from the production process to

the affected individuals; (iii) the human conditions.

These are related and the factors which can influence them are shown in Fig. 1. In order to design suitable policies for the control of such impact, it is

necessary to know how important it is. It would be quite possible to enforce legal controls which prevented all such impact, either by placing severe restrict- ions over the methods which may be applied in agricultural production or by zoning areas so that there were no residential areas adjoining those in which agricultural product ion was taking place. However, the costs which such policies would cause would be almost certain to outweigh any possible benefits. Nevertheless, in some countries control is exercised over the product ion of livestock, by laying down certain distances which must be left between

Agricultural Conditions Human Conditions

I FARM I passage of externality ~ HOUSEHOLD "l

Influencing factors :

Scale and type of operation distance perception of externality

production methods atmospheric ability to avoid

legal controls conditions external cost

nature of number of people external cost affected

Fig. 1. Factors influencing the scale of local farm impact.

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residential housing and livestock units or manure spreading (see for instance Anderson and Aalund, 1975). In the United Kingdom, some control is exercised over agricultural building, especially where these are not 'requisite for the use of the land'.

Ideally the cost of such impact would be evaluated in pounds and pence so that the benefits from a reduction in impact could be compared with the cost of control policies and so indicate their possible value. Approaches to the evaluation of the external costs of agricultural practices have been considered elsewhere (Hodge, 1976a). However, the possible ways in which estimates of costs may be obtained, such as through changes in proper ty values, expenditures made to avoid the costs and the costs implied by Government actions, are not available in this case. Nevertheless, it would still be of value to examine the extent and nature of local farm impact and to gain some measure of its scale, albeit one which is not directly comparable with other expenditures, but one which could at least allow the comparison of the impact of different livestock enterprises.

In the case of nuisance caused by intensive livestock production, there exists no satisfactory method of measuring the physical level of the factors causing the nuisance. The level of nuisance in such cases can only be estimated by means of surveys of those who are suffering from it. This type of measure therefore depends entirely upon the perceptions of those individuals. If they are asked whether they consider that they are caused a nuisance or not and variables are recorded which relate to each individual response, a discriminant function can be calculated which allocates each individual with a score indicating the extent to which he is in a position to be caused a nuisance, based on the perceptions of all the individuals in the survey. This possible approach is applied to data collected in two surveys carried out around farms in the south of England.

THESURVEYS

Surveys were carried out around two mainly livestock farms (A and B). In each case for ty households were randomly selected from within half a mile and a quarter of a mile of the farm boundaries, respectively. Details of the two surveys are given by Hodge (1976b). The questionnaire which was used included questions about employment , size of household, area of background, income and knowledge of farm activities as well as questions about whether any nuisance had been experienced, its nature and what action, if any, had been taken because of it. Lastly some questions a t tempted to induce a financial evaluation of the cost of the nuisance from the respondent. The interview was not directed at any particular member of the household, and in fact both wives and heads of households were interviewed. The distances and directions of the household from the actual farm unit and from the farm boundary were also recorded. Of the eighty households, there was one non-response, another interview not being carried out as it was felt that an unwillingness to be inter-

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viewed about the impact of the farm activities indicated a lack of concern about the subject. In certain other interviews some questions, especially those concerning income, were not answered.

THE FRAMEWORK

The fact of whether an individual around a farm considered that he had experienced any nuisance caused by that farm, divided the total local residents into two groups. In discriminant analysis, a linear combinat ion of independent variables, which measure characteristics on which two or more groups may be expected to differ, can be used to place each case into one of the groups. The discriminating variables are combined into a linear discriminant function which gives a discriminant score for each case. The function is of the form

Di = d i l Z l + di2Z2 + .... . + d i p Z p

where D i is the discriminant score on the discriminant function i. T h e d i ' s are

weighting coefficients and the Z's the standardized values of the p discriminating variables.

The parameters of this function are estimated so as to optimise the classification criterion between the two groups so that the probabili ty of each case being correctly classified is maximised. A consideration of the derivation of the linear discriminant function may be found in Kendall (1972). The size of the discriminant score is used to place each case into one of the groups. However the distribution of the scores for each group may overlap and so there remains a chance that some cases may be wrongly assigned. The number wrongly assigned depends on the power of the variables to accurately discriminate between the two groups.

Each discriminating variable is standardized and weighted, the weighted coefficients indicating the extent to which each variable contributes towards the separation of the two groups in the final discriminant function. The function can be used to assign previously unclassified cases to one of the groups. One measure of the significance of the analysis is given by the percentage of cases which are correctly classified, although this measure has been criticised by Frank et al. (1965). A further test is given by using part of the data for the computat ion of a discriminant function and classifying the remaining cases on this basis. An example of the use of discriminant analysis is in Willis (1973), where it was used in a s tudy of the development potential of villages in the Northern Pennines.

The present analysis was carried out using the Statistical Package for the Social Sciences (Nie et al., 1975). A stepwise procedure was adopted. This began with the single best discriminating variable (according a minimum Wilks' lambda criterion in this case). A second discriminating variable was selected as the variable best able to improve the discrimination criterion in combinat ion with the first variable, etc. At the end of the analysis the programme printed out the variables in the order in which they were entered,

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the significance of each variable in the analysis, and the standardized co- efficients for each variable in the discriminant function. An opt ion in the programme was used which printed out each case, its discriminant score and the chance of it being classified into each group. The total number of cases in each group according to whether the respondent had experienced nuisance or not was compared with the number of cases in each group as determined by the discriminant score, and the percentage of cases correctly classified was also shown.

The analysis used cases from both surveys. Cases which included missing values were suppressed, leaving 60 cases of which 14 had experienced some nuisance (Group 1) and 46 which had not (Group 2).

Twelve variables were hypothesised as having a possible influence on whether or not a nuisance was experienced. As high correlations among the independent variables should be avoided (Morrison, 1969), only one variable was included as a measure of distance of the household from the farm. One dummy variable was added to allow for the influence of each individual farm situation on the t w o surveys. Many of the variables, while contributing to the discriminating power of the function in this particular situation, were only of low significance, although because of the low sample size and of the assumption of normality required for the tests of significance, these tests are unlikely to be accurate.

In this example, the discriminant function classified 83.3% of the cases into the correct groups, as shown in Table I. There was overlapping of the discriminant scores calculated for the cases in each of the two groups. This can be seen in Fig. 2. Discriminant functions were also calculated us ingthe data from one

2 O

1 8

16

ul

B ~0

.o 8

5o 4

2

0

I

4 I I D i s c r i m i n a n t I I s c o r e s I I I I

C e n t r o i d C e n t r o i d g r o u p 2 g r o u p 1

Fig. 2. F r e q u e n c y d i s t r i bu t ions o f d i s c r iminan t scores us ing da ta f r o m all cases.

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o f t he t w o surveys and t hen cases in t he o t h e r survey c lass i f ied on the basis of t he d i s c r i m i n a n t scores wh ich were given. The p r e d i c t e d ~ lass i f i ca t ion o f Survey B cases us ing Survey A d a t a and o f Survey A cases us ing Survey B d a t a

are s h o w n in Tab les II and I I I , r e spec t ive ly .

TABLE I

Predicted and actual groups of cases in the analysis

Actual Predicted group Total group

1 2

1 8 6 14 2 4 42 46

Total 12 48 60

TABLE II

Predicted classification of Survey B cases using the Survey A data (66.7% were correctly classified)

Actual Predicted group Total group

1 2

1 3 0 3 2 8 13 21

Total 11 13 24

TABLE III

Predicted classification of Survey A cases using the Survey B data (66.7% were correctly classified)

Actual Predicted group Total group

1 2

1 3 8 11 2 4 21 25

Total 7 29 36

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THE DISCRIMINATING VARIABLES

The standardised discriminant Coefficients and the estimated F values are given in Table IV. These estimates were calculated using data for all the cases.

The most significant variable in the function is the distance of the respondent 's house from the farm boundary. This is closely followed by the variable determining with which farm the respondent is associated. Whether anyone in the household spent all day in the house was of least importance and was barely retained in the analysis. The single variable which was the best discriminator was whether the individual knew how the effluent from the livestock unit was disposed of. In the final function, in combinatinn with the other variables, this was of less importance.

TABLE IV

Standardised discriminant function coefficients

F value

vat001 var002 var003 vat004 vat005 var006 var007 vat008 vat009 var010 vat011 var 012

Distance from boundary - 0.75 3.5 Direction of household from farm 0.23 1.4 Number of people in household 0.27 1.5 Length of time lived in house 0.53 3.8 Rural or urban background 0.33 2.1 Own or rent house -0 .15 0.3 Whether spend all day in house 0.04 0.02 Know type of farming -0 .10 0.1 Know how effluent disposed -0.17 6.4 Income group 0.25 0.9 Agricultural or non-agricultural employment -0.31 0.7 Farm A or B -0 .73 5.7

While it was not possible to separate the two groups with the available data, the analysis suggests the importance of locational factors over personal factors in determining whether the respondent considered that there was a nuisance. It also illustrates the considerable problems in determining why people experience nuisance and what factors influence this. This is shown by the estimated F values, only two of which are significant at the 5% level.

It is therefore possible that some of the variables used in this analysis may not be of great value in the prediction of cases into one of the two groups in analyses of other farms.

THE DISCRIMINANT SCORE

The discriminant score, while not being a measure of the actual nuisance which is caused, does represent a measure of the extent to which an individual

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is in a position to be caused nuisance, on the basis of the sensitivities of the other respondents in the sample. The relationship between the dfscriminant scores of those respondents who indicated that they had experienced nuisance and whether they had complained or had indicated that they were willing to pay to have the nuisance removed, is shown in Table V. There appeared to be some tendency for those who had actually taken action to have higher discrim- inant scores, although it would no t be expected that these would coincide exactly due to the different sensitivities of the individuals.

TABLE V

Analysis of cases which experienced nuisance

Case Discriminant Willing to pay Complained No. score to have nuisance

removed

21 2.553 X 40 2.475 ~ 34 2.103 ~ X 37 2.034 X X 36 1.828 ~ X 17 1.700 X 15 1.504 X X 71 1.165 X X 67 1.078 ~ X 6 0.974 X X

10 0.587 X X 69 0.574 X X 31 0.524 J J 25 0.016 X X

~/= Yes; X = No.

If individuals around a large number of farms could be surveyed, a more generally applicable discriminant funct ion could be calculated. This would give an individual score for each respondent which could be aggregated for each farm on the basis of the number of residents living within a given distance of the farm boundary and so provide a figure for the total impact of an individual farm. If these data were collected for a large number of farms it might then be possible to associate total discriminant scores with specific levels of disutility. On this basis the total discriminant score is estimated by

N •i=1 Di (I/Ps)

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where, D i -- discriminant score of the ith individual; Ps = proport ion of the populat ion in the survey area included in

the sample; N = sample size.

Thus for Farm A -- 10.85 X 1/0.051 = 213 and for Farm B = - 1 0 . 8 5 X 1/0.068 = - 1 6 0

With only two examples these figures are only relative to each other. The sum of the discriminant scores in any one analysis will be zero. With a large number of cases, this type of measure would have the advantage of being based on the preferences of a large number of individuals from a wide range of areas. It would not rely on the sensitivity of a small number of people who may take action with less provocation than the majority. The major difficulty lies in the fact that the variables which have been tested in the two surveys appear not to explain a great deal of the variation in nuisance experienced by local residents. This analysis has concentrated on the factors influencing the 'human conditions ' and has used a dummy variable to allow for the differences in the two farms. If a large number of farms could be used in the construction of a discriminant function, other variables influencing the extent of nuisance caused could be included. These would be likely to include the size of the enterprise, the intensity at which the animals are kept and the methods of which are employed for waste disposal, and would r~place var012 in the present analysis. (Aspects of this are considered by Hodge, 1976b.) On the basis o f a larger number of examples, it is anticipated that a more generally applicable function could be developed.

APPLICATION

Control of local environmental impact can take place at two stages: (a) prior to the development of livestock units when planning permission and/or grants are being sought, and (b) in the investigations which may be made into complaints which result from nuisance which has been caused. The method of analysis outlined here could have relevance in both these situations.

As ment ioned above, the discriminant score represents a measure of the extent to which an individual is in a position to be caused a nuisance and so its measurement does not require that this nuisance is actually taking place. Thus before a new livestock unit is introduced, the projected variables could be used to calculate a total discriminant score from an ex ante position, by means of a general discriminant function, which would give a (relative) figure for the impact of that farm, based on the perceptions of a large number of people in similar circumstances. In the light of the scores of livestock units already in production, specific scores could be related to situations causing practically no nuisance or intolerable amounts of nuisance, and planning permission granted or withheld on this basis. For cases falling between these two extremes, plans could be inspected for any simple alterations which could reduce the expected nuisance, especially where such changes would

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cause little or no cost, and final decisions made in the light of the gains which are expected to result from their implementation.

When individuals complain about the nuisance which is caused by a product ion process, the actual level of cost which they are experiencing may vary considerably. The application of the discriminant function can provide a comparison of the nuisance being caused by this unit with that being caused by others, and therefore indicate the extent to which intervention in this case is justified.

In both these types of situation, care must be taken to allow for any special circumstance which may influence the extent of nuisance, which has not been allowed for in the discriminant function. Of special importance in this respect is the distribution of the nuisance. In simply summing the discriminant scores, the underlying assumption is that one unit of disutility to n individuals is equivalent to n units of disutility to one individual. This is clearly not necessarily the case and so a consideration of the distribution of the impact of any particular enterprise must be associated with a measure of the discriminant score.

In order for the function to be readily applicable in the two situations considered above, the variables selected would need to be relatively easily available in both an ex post and an ex ante situation. On this basis, some of those considered in the present analysis might be dropped because of their low significance and because of the survey work involved. Thus, whether the respondent spends all day in the house and whether the house is owned or rented would be unlikely to be retained. Also, from an ex ante position, questions concerning the respondents ' knowledge of the farm activities could not be asked. Some of the remaining variables could be estimated from local maps, e.g. the direction and distance of households so that only a small number of variables would need to be collected by means of interviews.

CONCLUSION

A method of analysing and evaluating the impact which livestock units have on local residents has been considered. This has been applied to two farms, but it is felt that more extensive survey work could allow the results to be more generally applicable. However, lack of time and resources has prevented the undertaking of a large number of surveys to test this. Nevertheless, the framework appears to provide a systematic method of screening plans for livestock enterprises before they begin product ion and of comparing the environmental impact of existing livestock enterprises. Once a general discriminant function has been produced, the method of application would be relatively straightforward. It is likely that the function would need to be updated periodically to allow for the changing perceptions and preferences of residents living in rural areas. It may also be necessary to apply different functions in different areas.

This procedure could also be applied to other product ion processes and

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environmental changes where there is no direct way of quantifying the en- vironmental impact. In situations where individuals are able to take actions as a result o f some form of environmental impact, it could be more satisfactory to use this as a criterion for dividing those affected into two groups. How- ever, in this case, such an option was not available.

ACKNOWLEDGEMENTS

The research for this paper was carried out while at Wye College, University of London. The author is grateful for the financial assistance of the Social Science l~esearch Council.

REFERENCES

Andersen, ~I. and Aalund, O., 1975. Intensive animal production in Denmark: some environmental aspects. Agric. Environm., 2: 65--73.

Frank, E.F~, Mauey, W.F. and Morrison, D.G., 1965. Bias in multiple discriminant analysis. J. Market. Res., 2: 250--258.

Hodge, I.D,, 1976a. Social costs in agricultural practice: some possible approaches to their evaluation. J. Environ. Manage., 4 (3), 225--240.

Hodge, I.Di, 1976b. External costs of agricultural practices, with special reference to intensiv e livestock production. Unpublished Ph. D. Thesis, Wye College, University of London;

Kendall, M.~G., 1972. A Course in Multivariate Analysis. Griffin, London, 185 pp. Morrison, D.G., 1969. On the interpretation of discriminant analysis. J. Market. Res., 6:

156--168. Nie, N.H., Hull, C.H., Jenkins, J.G., Steinbrenner, K. and Bent, D.H., 1975. Statistical

Package for the Social Sciences, 2nd edition. McGraw-Hill, New York, 675 pp. Willingar, H., 1974. Odour and pathogen control from intensive animal and poultry

husbandry in austria. Agric. Environm., 1 : 39--50. Willis, K.G., 1973. Economic policy determination and evaluation in the North Pennines.

Research Monograph No. 3, Agricultural Adjustment Unit, University of Newcastle upon Tyne, 60 pp.