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Confidence intervals for the cross-validated multiple correlation in predictive regression models
298
J PROD INNOV MANAG 1986;4:292-306
drawn in terms of a series of propositions or hypotheses, 14 altogether. These are summarized in paraphrased format below. A. Determinants of how much integration is required 1. Organizational strategy requirements: the need for organization is related to the aggressiveness of the firm's strategy. The perceived need for integration declines as the firm's stance shifts from actively prospecting for new product/market opportunities to passively reacting to the initiatives of others. 2. Environmental uncertainty requirements: the greater the environmental uncertainty (i.e., the perceived inability to anticipate changes in major external events), the greater the felt need for R&D/marketing integration. B. Determinants of how much integration is achieved 1. Organizational structure: the lower the degree of formalization (i.e., emphasis on following rules and procedures) and the lower the concentration of power (i.e., the degree of centralization), and the greater the degree of employee participation in the new product decision, the greater the degree of integration that will be achieved. 2. Role of senior management: the more senior management encourages risk-taking, the more R&D and marketing managers perceive they are jointly rewarded for new product success, the greater the formal recognition by senior management of the need for integration, and the more harmonious R&D/marketing operating characteristics (i.e., early and continuous joint involvement), the greater the degree of integration that will be achieved. 3. Sociocultural differences: the greater the similarity between R&D and marketing managers with respect to their professional/bureaucratic orientation, with respect to their tolerances for ambiguity, with respect to their perspectives on time, and with respect to the types of projects preferred, the greater the degree of integration that will be achieved. C. Integration and innovation success 1. The greater the gap between the degree of integration ideally required and actually achieved, the lower the probability of innovation success. The discussion concludes with a short but unusually good appendix, simplifying the discussion of such points as the meaning of integration and the various
ABSTRACTS
types of innovation strategies. Also summarized are comments from the literature about the influence of senior management on the R&D/marketing relationship. The two pages of references are also unusually good and, as might be expected, tie in well with the discussion.
Confidence Intervals for the CrossValidated Multiple Correlation in Predictive Regression Models, Robert L. Fowler, Journal of Applied Psychology (1986), pp. 318-322. (RRH)
Traditionally, cross-validation of a regression model is performed by splitting the sample into two groups: the calibration group and the prediction group. A regression model is then developed based on the calibration group and is then cross-validated using the prediction group. To evaluate the fit for the model, the population multiple correlation, p, and the population cross-validated multiple correlation, Pc, are estimated. Recently, interest has arisen in deriving formulae for estimating p and Pc analytically. Usually, in the applied fields, the observations on both predictor and criterion variables are drawn randomly, and it is necessary to develop confidence intervals for the validity coefficients p and Pc- This article discusses the two different methods for generating such confidence intervals using analytically derived ps and pcs. First, two models proposed by Cattin (Philippe, Estimation of the predictive power of a regression model, Journal of Applied Psychology 4:407-414 (1980)) for estimating p and Pc are evaluated. It is then shown that the confidence intervals obtained through 152 -+ 2(variance)l/2 proposed by Cattin are not accurate (i.e., the probability that the confidence interval would contain the parameter is less than half of the normal confidence statement). It is not necessary to obtain unbiased estimates for p and Pc, for developing a confidence interval, or to obtain confidence limits which are equidistant from the point estimates. The following are two methods for the fixed-predictors and random-predictors models are proposed. Fixed-Predictors Model: an existing method is uti-
ABSTRACTS
lized for normalizing the noncentral F distribution to estimate the noncentrality parameter h = N p 2 / ( 1 - p2) using N observations, K predictor variables, R, the coefficient of determination, and Z, the standard normal deviate. This estimate, L, is then used to calculate the 152 and 152 and their confidence intervals. Random-Predictors Model: a quadratic formula is developed as a function of L, N, and K. The roots of this quadratic expression are then utilized to establish the upper and lower confidence limits for the random predictors case. Finally, comparisons are made between the proposed models and the models presented by Cattin in order to demonstrate the efficiency of this approach.
Understanding the Diffusion Process for Technology-Intensive Products, Adil T. Talaysum, Research Management (July-August 1985), pp. 2 2 - 2 6 . ( C M C )
Diffusion refers to the spread of a new technology within the universe of potential adopters. Technology management has placed inadequate emphasis on managing the diffusion of new technologies. Planning for diffusion is an integral part of new products management, and should extend well beyond the initial marketing of the product. The classical diffusion model presents an S-shaped adoption curve, based on an assumed relationship between the number of potential users who have adopted it relative to the total number of potential users and those yet to adopt it. But this model has some inherent limitations. First, it is very difficult, in advance, to estimate the value of the innovation to various users. Experience is usually inadequate prior to marketing. Second, the model treats the innovation as univariant, whereas managers know that once the new product is introduced, competitors are likely to develop more sophisticated and/or less costly versions. Third, the mathematics of the function requires that we know the ceiling of the adoption percentage, again something that is rarely forecastable in advance. An alternative framework for diffusion planning is
J PROD INNOV MANAG 1986;4:292-306
299
the contribution of this article. The author urges that diffusion be conceived as a series of changes in the array of prospective users as affected by improvements in the operating characteristics of the technology, the emergence of new areas of application, changes in economic appeal of the technology, and changes in needs, resources, government controls, incentives, etc. Thus the ultimate diffusion curve for the technology may be conceived as the aggregation of a series of smaller diffusion curves (spread out over time). Each smaller curve represents adoption in a subpopulation, or in one use or user category. The shape of this cumulative diffusion curve is determined by the expansion in the universe of prospective uses/users and by the speed of their individual adoptions. Each of these subpopulation curves is S-shaped, and so is the overall curve, though with irregularity that comes with summation of the diverse subgroups. The diffusion of the CT scanner in the hospital industry is given as an example of this process. There were four subpopulations:
A small group of very large hospitals. These hospitals were the leading research centers in the nation and were potential adopters from the time of the technology's first availability. The large nonresearch hospitals requiring significant clinical utility. With large patient bases, they entered the universe subsequently, after improvements with respect to clinical applications were made to the initial technology. The medium to large hospitals with small patient bases. These hospitals awaited significant extensions of the clinical utility of CT scanners before they could enter the universe of potential adopters. Medium-scale hospitals that could not become potential adopters until the development of relatively inexpensive scanners and mobile scanners.
New products managers should plan to implement appropriate modifications to the technology in order to effect an orderly and profitable entry of subpopulations into the total group of potential adopters.
J PROD INNOV MANAG 1986;4:292-306
drawn in terms of a series of propositions or hypotheses, 14 altogether. These are summarized in paraphrased format below. A. Determinants of how much integration is required 1. Organizational strategy requirements: the need for organization is related to the aggressiveness of the firm's strategy. The perceived need for integration declines as the firm's stance shifts from actively prospecting for new product/market opportunities to passively reacting to the initiatives of others. 2. Environmental uncertainty requirements: the greater the environmental uncertainty (i.e., the perceived inability to anticipate changes in major external events), the greater the felt need for R&D/marketing integration. B. Determinants of how much integration is achieved 1. Organizational structure: the lower the degree of formalization (i.e., emphasis on following rules and procedures) and the lower the concentration of power (i.e., the degree of centralization), and the greater the degree of employee participation in the new product decision, the greater the degree of integration that will be achieved. 2. Role of senior management: the more senior management encourages risk-taking, the more R&D and marketing managers perceive they are jointly rewarded for new product success, the greater the formal recognition by senior management of the need for integration, and the more harmonious R&D/marketing operating characteristics (i.e., early and continuous joint involvement), the greater the degree of integration that will be achieved. 3. Sociocultural differences: the greater the similarity between R&D and marketing managers with respect to their professional/bureaucratic orientation, with respect to their tolerances for ambiguity, with respect to their perspectives on time, and with respect to the types of projects preferred, the greater the degree of integration that will be achieved. C. Integration and innovation success 1. The greater the gap between the degree of integration ideally required and actually achieved, the lower the probability of innovation success. The discussion concludes with a short but unusually good appendix, simplifying the discussion of such points as the meaning of integration and the various
ABSTRACTS
types of innovation strategies. Also summarized are comments from the literature about the influence of senior management on the R&D/marketing relationship. The two pages of references are also unusually good and, as might be expected, tie in well with the discussion.
Confidence Intervals for the CrossValidated Multiple Correlation in Predictive Regression Models, Robert L. Fowler, Journal of Applied Psychology (1986), pp. 318-322. (RRH)
Traditionally, cross-validation of a regression model is performed by splitting the sample into two groups: the calibration group and the prediction group. A regression model is then developed based on the calibration group and is then cross-validated using the prediction group. To evaluate the fit for the model, the population multiple correlation, p, and the population cross-validated multiple correlation, Pc, are estimated. Recently, interest has arisen in deriving formulae for estimating p and Pc analytically. Usually, in the applied fields, the observations on both predictor and criterion variables are drawn randomly, and it is necessary to develop confidence intervals for the validity coefficients p and Pc- This article discusses the two different methods for generating such confidence intervals using analytically derived ps and pcs. First, two models proposed by Cattin (Philippe, Estimation of the predictive power of a regression model, Journal of Applied Psychology 4:407-414 (1980)) for estimating p and Pc are evaluated. It is then shown that the confidence intervals obtained through 152 -+ 2(variance)l/2 proposed by Cattin are not accurate (i.e., the probability that the confidence interval would contain the parameter is less than half of the normal confidence statement). It is not necessary to obtain unbiased estimates for p and Pc, for developing a confidence interval, or to obtain confidence limits which are equidistant from the point estimates. The following are two methods for the fixed-predictors and random-predictors models are proposed. Fixed-Predictors Model: an existing method is uti-
ABSTRACTS
lized for normalizing the noncentral F distribution to estimate the noncentrality parameter h = N p 2 / ( 1 - p2) using N observations, K predictor variables, R, the coefficient of determination, and Z, the standard normal deviate. This estimate, L, is then used to calculate the 152 and 152 and their confidence intervals. Random-Predictors Model: a quadratic formula is developed as a function of L, N, and K. The roots of this quadratic expression are then utilized to establish the upper and lower confidence limits for the random predictors case. Finally, comparisons are made between the proposed models and the models presented by Cattin in order to demonstrate the efficiency of this approach.
Understanding the Diffusion Process for Technology-Intensive Products, Adil T. Talaysum, Research Management (July-August 1985), pp. 2 2 - 2 6 . ( C M C )
Diffusion refers to the spread of a new technology within the universe of potential adopters. Technology management has placed inadequate emphasis on managing the diffusion of new technologies. Planning for diffusion is an integral part of new products management, and should extend well beyond the initial marketing of the product. The classical diffusion model presents an S-shaped adoption curve, based on an assumed relationship between the number of potential users who have adopted it relative to the total number of potential users and those yet to adopt it. But this model has some inherent limitations. First, it is very difficult, in advance, to estimate the value of the innovation to various users. Experience is usually inadequate prior to marketing. Second, the model treats the innovation as univariant, whereas managers know that once the new product is introduced, competitors are likely to develop more sophisticated and/or less costly versions. Third, the mathematics of the function requires that we know the ceiling of the adoption percentage, again something that is rarely forecastable in advance. An alternative framework for diffusion planning is
J PROD INNOV MANAG 1986;4:292-306
299
the contribution of this article. The author urges that diffusion be conceived as a series of changes in the array of prospective users as affected by improvements in the operating characteristics of the technology, the emergence of new areas of application, changes in economic appeal of the technology, and changes in needs, resources, government controls, incentives, etc. Thus the ultimate diffusion curve for the technology may be conceived as the aggregation of a series of smaller diffusion curves (spread out over time). Each smaller curve represents adoption in a subpopulation, or in one use or user category. The shape of this cumulative diffusion curve is determined by the expansion in the universe of prospective uses/users and by the speed of their individual adoptions. Each of these subpopulation curves is S-shaped, and so is the overall curve, though with irregularity that comes with summation of the diverse subgroups. The diffusion of the CT scanner in the hospital industry is given as an example of this process. There were four subpopulations:
A small group of very large hospitals. These hospitals were the leading research centers in the nation and were potential adopters from the time of the technology's first availability. The large nonresearch hospitals requiring significant clinical utility. With large patient bases, they entered the universe subsequently, after improvements with respect to clinical applications were made to the initial technology. The medium to large hospitals with small patient bases. These hospitals awaited significant extensions of the clinical utility of CT scanners before they could enter the universe of potential adopters. Medium-scale hospitals that could not become potential adopters until the development of relatively inexpensive scanners and mobile scanners.
New products managers should plan to implement appropriate modifications to the technology in order to effect an orderly and profitable entry of subpopulations into the total group of potential adopters.