A FA.MILY OF MODELS INVOLVING INTERSECTING STRAIGHT LINES AND CONCO.'MITANT EXPERIMENTAL DESIGNS USEFUL IN EVALUATING RESPONSE TO FERTILIZER NUTRIENTS'

For many cropping situations, especially in developinig countries, quadratic surfaces do not fit the responses of cer tain crops to fertilizer. Use of the seconid or der designs with stanidard statistical anid econiomic interpretive techniques may result in costly biases in the estimates of the optimal fertilizer rate. Also, there is a potential pollution problem. A family of linear-plateau models, coinsistiing of intersecting straight linies, is proposed for fitting fertilizer response data which exhibit a plateau effect. The regression coefficients are easily comptuted uisinig a desk calcutlator or computer, and the economic interpretations are simple. Techniques for fitting, parameter estimation, and economic interpretation are described. For mtulti-nutrtiienit experiments, a complete factorial experiment with a nulmber of levels of each nutrient is considered to be the best design foi both evaltuating the model and theii estimating the optimal ntutrient levels. Preliminary information may provide a basis for deciding which fertilizer nutrients are apt to produce response. In maniy soil-crop situations, only NTP or AT experiments are required, becatuse the other nutrients are already at adequiate levels; hence, the amotunt of experimental material may be redistributed by havinig fewer factors, bult more levels of each factor stu.died. Two cutrrently used fertilizer response designs, based on preliminary information on optimal nutrient levels, are described; a one-factor-at-a-time design has the disadvantage of providing no estimate of interaction. Several other designs are suggested. We recommend concenitratiing seveial tieatment levels in the vicinity of the aniticipated optimtum. Since the sloping phase of the response pattern is mole important thani the plateatu phase, it shouild receive more attention when distributitng treatment levels.