Heterogeneity Of Regression Research Articles

Model specification for nonlinearity and heterogeneity of regression in randomized pretest posttest studies: Practical solutions for missing data.

The randomized pretest posttest design is common in psychology, as is the corresponding missing data concern. Although missing data handling has seen advances over the past several decades, effective and practical solutions for handling missing data in randomized pretest posttest designs are lacking, particularly when assumptions of commonly used statistical models are violated. Although analysis of covariance can capture the average treatment effect with complete data, even when assumptions are tenuous, this becomes more difficult with missing data. This investigation fills this gap in the literature by comparing a variety of analysis models for estimating the average treatment effect under violations of linearity and homogeneity of regression slopes, when data are missing by several plausible, but understudied, missing at random patterns for randomized pretest posttest studies. Two missing data handling techniques, listwise deletion and multiple imputation, were considered. Listwise deletion provided maximum likelihood estimates (unbiased and appropriately precise) of the average treatment effect as long as the analysis model was appropriately specified to handle the violated assumption and the pretest mean was estimated using all cases. Although multiple imputation was effective as long as the imputation model was correct, the results highlight to the importance of model specification in the context of missing data. Importantly, the specific pattern of missing at random data had implications for results, emphasizing the need to consider the particular pattern of missingness beyond the general appropriateness of the missing at random assumption. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Supplemental Material for Model Specification for Nonlinearity and Heterogeneity of Regression in Randomized Pretest Posttest Studies: Practical Solutions for Missing Data

Supplemental Material for Model Specification for Nonlinearity and Heterogeneity of Regression in Randomized Pretest Posttest Studies: Practical Solutions for Missing Data

Analysis of Covariance in Randomized Experiments with Heterogeneity of Regression and a Random Covariate: The Variance of the Estimated Treatment Effect at Selected Covariate Values

Researchers detecting heterogeneity of regression in a treatment outcome study including a covariate and random assignment to groups often want to investigate the simple treatment effect at the sample grand mean of the covariate and at points one standard deviation above and below that mean. The estimated variances of the simple treatment effect that have traditionally been used in such tests were derived under the assumption that the covariate values were fixed constants. We derive results appropriate for a two-group experiment that instead presume the covariate is a normally distributed random variable. A simulation study is used to confirm the validity of the analytical results and to compare error estimates and confidence intervals based on these results with those based on assuming a fixed covariate. Discrepancies between estimates for fixed and random covariates of the variability of treatment effects can be substantial. However, in situations where the extent of heterogeneity of regression is like that typically reported, presuming the covariate is random rather than fixed will generally result in only a modest increase in estimated standard errors, and in some circumstances can even result in a smaller estimated standard error. We illustrate the new methods with an empirical data set.

Patterns of Regression in Breast Cancer after Primary Systemic Treatment.

Despite national guidelines, the evaluation of effects of primary systemic treatment (PST) in breast cancer is a complex challenge. Our aims were to evaluate the response patterns focusing on correlations of radiological and pathological tumor size, regression heterogeneity in different molecular subtypes, cellularity changes and the incidence of enlarged, multinucleated neoplastic cells related to therapy. Slides of pretreatment biopsies and resection specimens of consecutive cases were reevaluated focusing on heterogeneity of regression per whole slide, and 40x or 100x magnification fields. Alteration in cellularity and the presence of multinucleated tumor giant cells were noted. The correlation of pathological and radiological sizes and their alterations were analyzed by Spearman rank correlation. The present study included 106 tumors. A decrease in size (84.9%) and cellularity (76.4%) was noted in all molecular subtypes. Inhomogeneous regression was found in 45.3%, with minor inhomogeneity in the majority. Scatter pattern regression was seen only in 8 cases (7.5%). Significant correlations were found between the pathological and radiological sizes (p = 0.02), and between the alterations of cellularity and pathological and radiological size (p = 0.04; p = 0.03, respectively). Multinucleated tumor giant cells were noted in 17.9% (n = 19), nearly exclusively in cases treated with PST including taxanes. Regression inhomogeneity following PST is present in about half of the cases, and is not related to molecular subtypes. The evaluation of the maximum area of the tumor bed is recommended for the proper evaluation of regression. Multinucleated tumor giant cells are related to PST including taxane derivate, and may cause upgrading.

Stability Analysis of Bean Yields of Arabica Coffee Genotypes across Different Environments

An evaluation of stability of thirty Arabica coffee genotypes was carried out across different environments. The interaction of genotype by environment (G x E) across the different environments was highly significant. Both heterogeneity of regression and pooled deviation mean square from regression were highly significant. On this basis stability analysis was done using regression and AMMI models. On the basis of the analyses, different sets of genotypes were found as stable by the two models. Genotypes 7803A and 7803B, which were at the 13 th and 14 th ranks from thirty genotypes, were found as stable by the regression model. On the other hand genotypes 8143, 75187B and 8019, which were at the second, third and seventh ranks, were found as stable by the AMMI model. The discrepancy noticed in the two models in indicating the stable genotypes was largely attributed to their differences in accounting the interaction sum of squares. The result of the study is considered as one remarkable success in the history of Arabica coffee research as identifying stable genotype for multi-locations / diverse environments has long been a major challenge and in practice able for decades.

Prediction of Hevea progeny performance in the presence of genotype-environment interaction

Twenty two open-pollinated Hevea progenies from different parental clones of the Asian origin were tested at five sites in the Northwestern São Paulo State Brazil to investigate the progeny girth growth, rubber yield, bark thickness and plant height. Except for the rubber yield, the analysis of variance indicated highly significant (p<0.01) genotype x environment interaction and heterogeneity of regressions among the progenies. However, the regression stability analysis identified only a few interacting progenies which had regression coefficients significantly different from the expected value of one. The linear regressions of the progeny mean performance at each test on an environmental index (mean of all the progenies in each test) showed the general stability and adaptability of most selected Hevea progenies over the test environments. The few progenies which were responsive and high yielding on different test sites could be used to maximize the rubber cultivars productivity and to obtain the best use of the genetically improved stock under different environmental conditions.

Bayesian modelling strategies for spatially varying regression coefficients: A multivariate perspective for multiple outcomes

The modelling of spatially varying regression effects for multivariate mortality count outcomes is investigated. Alternative approaches to spatial regression heterogeneity are considered: the multivariate normal conditional autoregressive (MCAR) model is contrasted with a flexible set of priors based on the multiple membership approach. These include spatial factor priors and a non-parametric approach based on the Dirichlet process. A case study considers varying regression effects for a bivariate suicide outcome, namely male and female suicides in 354 English local authorities with social deprivation, social fragmentation and rurality as predictors.

Genotype-Environment Interactions in Wheat in the IV and Vsouth Argentinean Subregions

The objective of the present study was to evaluate the genotype X environment inter-action and its quantification by means of additive main effects and multiplicative interaction (AMMI) and joint linear regression analysis at the IV and Vsouth Argentinean wheat (Triticum aes-tivum L.) subregions. Grain yield data from 1992–1995 wheat regional trials network were ana-lyzed. The data were divided in early sowing date (late May - late June) and late one (during July to beginning of August). Nine genotypes and 50 environments (location by year combination) were evaluated at early sowing date and 8 genotypes and 44 environments were analyzed at late one. AMMI and Joint Linear regression analyses were employed. Regression heterogeneity was nonsignifiicant at neither of two sowing dates. This technique didn’t reveal the components of interaction. AMMI analysis, suggested the inclusion of the first three principal component analysis (PCA) for the early sowing date that accounted for 47.67, 29.41 and 12.24% of interaction sum of squares (SS), respectively, while two first PCA axes captured 44.20 and 21.33% of interaction SS, respectively, for the late one. The AMMI model retained 98.87% (early) and 96.64% (late) of the total SS. AMMI analysis proved to be a more efficient way of evaluating the GXE interactions than joint linear regression for the data set used here.

Genotype * sucrose interactions for 2,4-D-induced somatic embryogenesis in soybean (Glycine max L.).

Cotyledons isolated from immature embryos of 11 varieties of soybean were cultured on embryogenesis media containing 2, 4-D at 40mgl-1 and sucrose at 10, 20, 40, or 60gl-1. The number of somatic embryos per cotyledon was counted after 5 weeks of culture. Analysis of variance showed that the effects of genotype, sucrose concentration, and genotype×sucrose interaction were all highly significant. Further analysis of the genotype×sucrose interaction showed that the heterogeneity of regression among the varieties was significant. The variety mean and regression were significantly correlated, indicating that the 2 factors are not under separate genetic control. Nevertheless, these results suggest that embryogenic response to 2, 4-D and NAA seems to be under separate genetic control in soybean.

Study of Genotype x Environment Interaction for Forage Yield in Oat (Avena sativa L.) with Joint Linear Regression Analysis and AMMI Analysis.

Improvement of forage yield in oat (Avena sativa L.) depends on thorough understanding of the influences of genotype, environment and the genotype x environment interaction (G X E). The objetive of this study was to analyze G X E interaction in oat for biomass forage yield according two different models, joint linear regression analysis (JRA) and AMMI analysis. Twelve genotypes were grown in different environments during three years (1993-94-95) at the locations of La Dulce and La Plata, Buenos Aires Province, Argentina. The forage yield (dry matter yield Kg/ha) was determined at 60, 100 days after emergence and at ripening. Heterogeneity of regression in JRA was nonsignificant. Interaction sume of square accounted for by heterogeneity of regression were 12.08 % (three years mean). In contrast, the first principal component axis in AMMI was highly significant (P<.001). This first axis accounted for by 68.46 % of interaction SS (three years mean). The AMMI model was found tobe more effective than JRA analysis in accounting for GXE interaction under low environmental diversity The use of AMMI is recommended for the study of GXE effects in the oat breeding for forage yield.

Methodological Issues in Educational Performance and School Effectiveness Research: A Discussion with Worked Examples

There has been a growing awareness among educational researchers of the consequences of using data-analytic models that fail to account for the inherent clustered or hierarchical sampling structure of the data typically obtained. Such clustering poses special analytic problems related to levels of analysis, aggregation bias, heterogeneity of regression and parameter mis-estimation, with important implications for the correct interpretation of effects. This paper compares the results obtained from fitting single-level and multilevel models to two hierarchically structured data sets designed to explain variation in student achievement. Emphasis is given to the crucial importance of fitting models commensurate with the sampling structure of the data to which they are applied.

Regression and AMMI Analyses of Genotype × Environment Interactions: An Empirical Comparison

AbstractJoint regression analysis (JRA) is a popular method for analyzing genotype × environment (G × E) interactions, but multivariate techniques such as AMMI (additive main effects and multiplicative interaction) analysis have been recently advocated. The objective of this study was to investigate and compare empirically the effectiveness of the two techniques under differing environmental diversity and numbers of environments, and when log‐transformed data were used for JRA. I analyzed grain yield data from three seasons of a regional bread wheat (Triticum aestivum L.) yield trial, grown at 30 to 40 sites. Sites were split into irrigated‐high rainfall and rainfed‐low rainfall groups. Three equal‐size samples differing in environmental diversity and three similar diversity samples differing in numbers of sites were also formed. Both raw and log10‐transformed data were used for JRA. The fitting mode of the MATMODEL program (version 2.0) was used on raw data for AMMI analysis. Percentages of interaction sum of squares (SS) accounted for by heterogeneity of regression in JRA were generally low (mean = 11%) and unaffected by diversity of the samples, but inversely related to number of sites in the similar‐diversity samples. In contrast, percentages of interaction SS accounted for by first principal components in AMMI analyses were generally high (mean = 37%) and unaffected by diversity or number of sites in the samples. These percentages were always higher for AMMI than for JRA, regardless of whether log‐transformed data were used for JRA. The use of AMMI is recommended for detailed studies of G × E effects, especially for large regional or international trials.

Effect of cranial sympathectomy on circadian rhythms of cortisol, adrenocorticotropic hormone and melatonin in boars1

Following weaning at 24 +/- 1 d of age, crossbred boars were subjected to removal of the cranial cervical ganglia (GX, n = 8) or sham surgery (SHAM, n = 8). At 213 +/- 1 d of age, a catheter was inserted into a jugular vein or vena cava, and all boars were housed in environmentally controlled rooms at 22 degrees C with an equatorial photoperiod. After 2 wk of exposure to this photic environment, samples of plasma and serum were collected at hourly intervals for 24 h. The plasma was assayed for adrenocorticotropic hormone (ACTH) and the serum was assayed for cortisol and melatonin by RIA. The time-trends for all three hormones were described by regression models, which were tested for heterogeneity of regression between SHAM and GX treatments. The circadian rhythm of cortisol in serum was similar for SHAM and GX treatments. The profiles of ACTH were also similar between the two treatments, but circadian changes in concentrations of ACTH paralleling those of cortisol were not evident in either treatment. Overall, concentrations of ACTH were reduced (P = .06) for GX boars compared to SHAM boars. The time-trends of melatonin in serum differed (P less than .001) for GX and SHAM treatments, with a nocturnal rise in melatonin evident in some SHAM boars but not in GX animals. Four SHAM boars had profiles of melatonin that obviously entrained to the light-dark cycle. None of the boars in GX treatment had elevated concentrations of melatonin in serum during the dark period, relative to concentrations during the light.(ABSTRACT TRUNCATED AT 250 WORDS)

Specific and General Adaptation and Yield Stability of Wheat (Triticum aestivum L.) Genotypes

AbstractMean grain yield performance of 12 wheat and one triticale genotypes were measured at four locations over four consecutive years, using a randomized complete block design with four replications. The genotypes used were commercial cultivars and advanced lines from different wheat breeding projects located in different areas in Iran. Two locations were in semiarid regions and the other two locations in the temperate zones.The combined analysis of variance indicated highly significant genotype‐environment (GE) interactions. From combinations of locations and years three sets of environments were generated. Set I and set II, each, consisted of eight environments (two locations and four years) representing semiarid and temperature environments, respectively. Set III consisted of 16 environments including both semiarid and temperate conditions. Set I and set II were used to measure specific adaptation of the genotypes while set III was employed for measuring general adaptation.The methods of Eberhart and Russell (1966) were used for partitioning GE interactions. The mean square associated with the heterogeneity of regression was highly significant under all sets of environments. These observations indicated that a major part of GE interaction could be accounted for by differences in the regression of the individual genotypes.All the genotypes had significant regression mean square under set I, set II, and set III environments, with the exception of two genotypes under set II. However, mean yields, regression coefficients, and the mean squares associated with deviation from regression greatly varied over the sets of environments.Only three genotypes, a commercial cultivar and two new advanced line, were identified as having specific adaptation and yield stability to semiarid environments.Among all the genotypes, only a commercial cultivar was identified as adapted and stable to temperate conditions. Two of the three genotypes which were adapted to semiarid environments also showed general adaptation to set III environments. However, the mean yield of these two genotypes under semiarid conditions (set I) were significantly greater than their respective mean yields under set III environments. Thus, wider adaptability was compensated by lower mean yield.The present study indicates that, while a wide range of environments is necessary and recommended for measuring general adaptation reactions and yield stability of various genotypes, one should not ignore the possibility of finding some genotypes with specific adaptation to specific environments and thus maximizing yield production. Stable genotypes with general of specific adaptation should be utilized in breeding projects in order to develop even more desirable lines.

Prostaglandin F2α as the Luteolysin in Swine: VI. Hormonal Regulation of the Movement of Exogenous PGF2α from the Uterine Lumen into the Vasculature1

To test the endocrine-exocrine theory of maternal recognition of pregnancy in the pig 16 gilts were assigned randomly to a 2 X 2 factorial involving pretreatment with sesame oil (SO) or estradiol valerate (5 mg; EV) injected on Days 11 through 14 of the estrous cycle and an intrauterine injection of saline (5 ml; SA) or prostaglandin F2 alpha (50 micrograms; PGF) on Day 14. Peripheral blood samples were collected for 120 min postinjection and analyzed for 15-keto-13,14-dihydro-PGF2 alpha (PGFM). PGFM concentrations were lower in EV than SO gilts (438 vs. 844 pg/ml; p less than 0.05). There was heterogeneity of regression between EV and SO gilts (p less than 0.01), with EV gilts having a slower release of PGF from the uterine lumen into the vasculature. Prostaglandin F2 alpha did not increase mean PGFM concentrations (p greater than 0.10), but resulted in an altered temporal pattern of PGFM (p less than 0.05) compared to SA gilts. There was an interaction between the two treatments over time, with EV-PGF gilts demonstrating a slower, more gradual release of PGFM than SO-PGF gilts. To test whether prostaglandins of the E series were involved in this mechanism, gilts were assigned to two 4 X 4 latin squares balanced for residual effects and treated with saline or flunixen meglumine (Banamine). Each gilt was treated with four PGE:PGF infusion sequences (SEQ) in each uterine horn: phosphate-buffered saline (PBS; PBS-SEQ), PGE1 (50 micrograms), PGE2 (50 micrograms), and PGE1 (25 micrograms) + PGE2 (25 micrograms) (PGE-SEQ), with each infusion followed 15 min later by PGF (25 micrograms).(ABSTRACT TRUNCATED AT 250 WORDS)

YIELD STABILITY IN INTERCROPPING STUDIES OF SORGHUM OR MAIZE WITH COWPEA OR COMMON BEAN UNDER DIFFERENT FERTILITY LEVELS IN NORTHEASTERN BRAZIL

Experimental evidence on yield stability of intercropping is sparse. This work was carried out to examine the stability of four intercrop patterns: maize (Zea mays L.)/cowpea (Vigna unguiculata (L.) Walp); maize/common bean (Phaseolus vulgaris L.); sorghum (Sorghum bicolor (L.) Moench)/cowpea; and, sorghum/common bean against their component crops. Twenty-one trials were established from 1974 to 1978. The mean relative yield advantage of intercropping patterns as indicated by the land equivalent ratio (LER) was 32%. The combined analysis of variance for the absolute total yields revealed that most of the pattern × environment interaction is accounted for by the heterogeneity of regressions. Pulses were less responsive to environmental change. However, cereals were more responsive to improvement in the environment resulting in increased yield. The regression lines of the intercropping patterns and sole cereals were closer to each other, due to the low yield contribution of the pulses to the intercropping total yield. However, the slopes of the intercropping pattern lines were closer to b = 1.0. On the basis of mean yield and regression slope, it was demonstrated that sole cereals or intercropping have better performance stability than sole pulses in northeastern Brazil.Key words: Stability, intercropping, sorghum, maize, cowpea, common bean

Genotype × Environmental Interactions on Reproductive Traits of Bovine Females. III. Seasonal Variation in Postpartum Reproduction as Influenced by Genotype, Suckling and Dietary Regimen3

We examined the effect of season of calving (winter = October to March, summer = April to September) on postpartum reproductive traits by analyzing six data sets in which cows calved throughout the year. In two experiments, with suckled and nonsuckled cows, animals that calved in winter had longer (P less than .01) intervals from parturition to first estrus (IE) than those that calved in summer. Multiple regression analysis [model; IE = y + b1 (calving date) + b2 (calving date)2] indicated that the relationship between calving date and IE was less for nonsuckled cows than for suckled cows because there was heterogeneity of regression (P less than .005) between groups. A similar seasonal difference and calving date X suckling status interaction (P less than .10) was observed in a third experiment. Another experiment involved Holstein cows ranked for genetic ability for milk production. Cows with genetic ability for high milk production and calving in summer tended (P less than .12) to have shorter IE than winter-calving cows. Genetically low producing cows did not show this tendency and there was heterogeneity of regression (P less than .10) between groups. In two experiments cows were fed diets either low or high in energy and data were analyzed for three consecutive postpartum periods (PP1, PP2, PP3) beginning after first calving. In PP1 of one experiment, intervals to first ovulation, estrus and conception were longer in winter than in summer. The multiple regression equation between calving date and IE was significant (P less than .10) only for cows fed diets low in energy. There was no significant relationship between calving date and IE in PP2 or PP3. In the other experiment, there were not enough winter-calving cows to make seasonal comparisons in PP1 and season did not significantly influence IE in PP2 or PP3. We concluded that, in general, winter-calving cows appeared to take longer to regain reproductive competence after calving than summer-calving cows. Differences between seasons tended to be greater for suckled cows, cows with genetic ability for high milk production, primiparous cows and cows fed diets low in energy.

Testing for regression homogeneity under variance heterogeneity.

One of the assumptions underlying the F test of parallelism of two or more regression lines is that the within-group residual variances are homogeneous. In the present two-group Monte Carlo investigation, the effect of violating (his assumption was examined for F, a large-sample chi-square approximation (C/0), and an approximate F test (F*). In terms of Type I error probabilities, the standard F test performed acceptably well as long as sample sizes were equal. This was not true when sample sizes were unequal, with F* proving to be clearly superior. The pattern of results paralleled exactly what is known about the robustness of the F test when testing for mean differences in the presence of unequal variances. Recommendations for the applied researcher follow directly from the findings, Questions concerning the parallelism (homogeneity) or nonparallelis m (heterogeneity) of K independent regression lines are relevant in at least two common empirical research situations. First, homogeneity of regression is an underlying assumption of classical analysis of covariance (ANCOVA; see Elashoff, 1969, and Glass, Peckham, & Sanders, 1972). Second, regression heterogeneity is of principal concern to researchers who are interested in discovering Aptitude X Treatment interactions (ATIs; see Cronbach & Snow, 1977). In either case, a statistical test of the homogeneity-ofregression hypothesis can be conducted— and usually is in the ATI situation. Moreover, the F test associated with this hypothesis is itself founded on several assumptions, including (among others) independence, normality, and homoscedasticity of the residuals. The focal assumption of the present investigation is that of equal residual variation The authors wish to thank Scott Maxwell, Penelope Peterson, and two anonymous referees for their helpful comments on an earlier draft of the manuscript. Thanks are also due Kathy Tobin for typing the manuscript. Requests for reprints should be sent to Joel R. Levin, Department of Educational Psychology, 1025 W. Johnson Street, University of Wisconsin, Madison, Wisconsin 53706. in the K populations. This assumption means that the variation of the dependent variable (y) about the regression line (F) is the same in each population. With the residual variance in the &th population defined as

Genotype-environment relationships for repening time in blackberries and prospects for breeding an early ripening cultivar for Scotland

When grown in Scotland, eight blackberry cultivars of diverse origin showed considerable variation in the dates when their first fruits ripened. These dates were determined in part by variation in the date of their first open flower and in part by variation in the number of days required from flowering to ripening. Genotype x environment interactions were important for both components, but especially for the second, where they could be attributed to heterogeneity of regressions against the environmental means. Temperature was considered the important environmental factor determining the number of days required from flowering to repening, and accumulated heat units successfully quantified the differences between cultivars for this component: cultivars required similar numbers of heat units in each season and there were no interaction effects. Heat units were not useful for study of flowering dates, however.

Adaptation of safflower genotypes Carthamus tinctorius L.

Adaptation reactions of 33 genotypes of safflower Carthamus tinctorius L. were studied under 7 different climatic conditions. The genotpyes were divided into two sets. Set I consisted of 15 genotpyes selected from the local populations. Set II had 15 introduced and local varieties. Three control genotpyes, Ute, Ferio, and Local Arak, were common to both sets.Genotpye-environment interaction was not significant for Set I but it was highly significant for Set II. Three environmental indices were obtained and used in the adaptation analyses of the genotpyes in Set II. One of the environmental indices, designated EI, was dependent on the genotypes of Set II. The other two indices, designated EI-1 and EI-2, were independent of the genotpyes of Set II. The methods of Eberhart and Russell (1966) were used in analyses of adaptation by Index EI and the methods of Freeman and Perkins (1971) for Indices EI-1 and EI-2.The mean square associated with genotype-environment interaction was partitioned into two components, heterogeneity of regression and its residual, under EI-1 and EI-2. Both components were highly significant for both cases. However, the mean square of heterogeneity of regression was equal to its residual under EI-1 and even smaller than its residual under EI-2. These observations indicate that a major part of genotpye-environment interaction can not be accounted for by differences in the regressions of the individual genotypes. As well as this overall test, individual regression analyses for single genotypes were also considered. None of the genotypes had significant regression mean square under EI-1. Only two introduced genotypes had significant regression mean squares when EI-2 was used. The overall test of equality of the slopes of the regression for the genotypes of Set II was rejected at the 1% level under EI. This test indicated that genotypes of Set II were significantly different in their association with the EI. The significant differences among the genotypes of Set II were also shown by an F test of the pooled deviation mean square divided by the pooled error mean square. Individual regression analyses for single genotpyes of Set II were considered under EI. Mixed adaptation reactions were observed for different genotypes. Among 18 genotypes of Set II, regression mean squares were significant for only 10 genotpyes. Therefore, it appeared that the dependent environmental indices are more useful than the independent environmental indices when statistical theory of regression is used in the analysis of adaptation. Observations in the present study were not in agreement with the hypothesis that the relation between the performance of different genotypes in the various environments and some measure of these environments is linear or nearly so.Among the 12 introduced genotypes, only one, Ute, was identified as stable and high-yielding. Among the 15 selected from the locally adapted populations, eleven did not differ significantly from Ute in mean yield but four exceeded Ute significantly in mean productivity. The present study thus indicates that the Iranian safflower breeding project has been successful in identifying genotpyes which give high and stable yields under diverse environmental conditions. It does not indicate that introduced and exotic germplasms are unimportant in the breeding projects; it is quite possible that still more desirable genotypes can be developed by incorporating introduced genetic variability into the local germplasm.