Piecewise Multiple Regression Research Articles

Examining features of how professional development and enactment of educative curricula influences elementary science teacher learning

AbstractThis research examines factors influencing elementary science teacher learning as they participate in professional development with and enactment of educative curricula in comparison with learning following limited professional development and enactment of traditional curricula. Using a randomized cluster design (125 teachers and 2,694 students in 4th—5th grades) that met the What Works Clearinghouse standards without reservations, teacher learning was conceptualized using four outcomes. Data were analyzed using standard single‐level multiple regression models and possible mediation models for the teacher outcomes were considered using piecewise multiple regression and path analytic approaches. Treatment group teachers experienced greater increases in content knowledge, views of science inquiry, beliefs about reform‐based teaching, and teaching self‐efficacy than comparison group teachers. The findings indicate that what teachers learn from the combination of professional development and teaching with educative curriculum varies according to what their knowledge and beliefs are on entering the experience. Surprisingly, high entry‐level self‐efficacy was associated not only with lower learning gains for the teachers, but also for their students. Finally, teachers' space science learning and that of their students are implicated as mediators of the positive effect of the professional development and educative curriculum enactment on teacher beliefs about reform science teaching. This work refines and extends a theoretical framework of teachers' participatory relationship with curricula.

Simulation scheme of dusk scene using piece-wise multiple regression based on time-series color-block images

Dusk and dawn are usually the most beautiful moments of the day, and are almost always too short for busy people nowadays to witness their coming. In this work, an efficient strategy for simulating a dusk scene of an outdoor scene image taken at other times before the sunset is presented. The strategy is a hybrid approach combining the piece-wise multiple regression (PMR) of data, discrete cosine transformation (DCT), and a look-up table algorithm. The process begins using a series of color-block images taken in the afternoon of a day. The best fitting functions of PMR for these color block images exist on separate planes (red, green, and blue) in the DCT domain individually. The reference databases of the DCT coefficients varying with respect to time are then established according to the best fitting functions of PMR. Finally, the dusk scene of an outdoor scene taken in the afternoon is synthesized by querying the reference database. The experiment results show that the presented algorithm can precisely simulate the desired dusk scene from a scene image taken in the afternoon.

Predicting Tenofovir Concentration on the Basis of Renal Factors Determined by Routine Tests

Although it has not caused overt renal damage in clinical trials, tenofovir disoproxil fumarate (TDF) has been associated with renal dysfunction in isolated cases. The objective of this study was to assess the TDF concentration with use of the glomerular filtration rate (GFR) and blood urea nitrogen (BUN) level. Serum creatinine (used to calculate GFR), BUN, and plasma TDF trough values were measured in 51 patient volunteers at pretreatment and post-treatment time points. The post-treatment GFR (post_GFR) and the difference between the pretreatment and post-treatment BUN levels (dif_BUN) were strongly related to TDF concentration. A piecewise multiple regression technique was applied to the nonlinear TDF distribution, revealing a significant association of the post_GFR and dif_BUN values with TDF concentration (P=0.002 and P= 0.003, respectively). Post_GFR values below 125 mL/min/1.73 m(2) and/or dif_BUN values below -3 mg/dL are predicted to cause a marked increase in the TDF concentration. The relationship between TDF and BUN is a new finding. Knowledge of the pretreatment and post-treatment serum creatinine and BUN levels is important for the safe clinical administration of TDF.

Microconsumer grazing and sources of limiting nutrients for phytoplankton growth: Application and complications of a nutrient‐depletion/dilution‐gradient technique

A series of eight nutrient‐deletion/dilution‐gradient experiments was performed in Castle Lake during summer 1993 to quantify and characterize microconsumer grazing and contributions of nutrient supply sources (external, cell quota, recycling) supporting phytoplankton production. Responses of net chlorophyll production rate to dilution under nutrient‐saturated conditions were frequently nonlinear, indicating saturation of micrograzer feeding at low biomass levels within the dilution gradient (dilutions of < 10–30% whole lake water). Despite feeding saturation, micrograzers exerted substantial grazing pressure on phytoplankton: microconsumer grazing coefficients (0.05–0.22 d–1, mean: 0.14 d−1) exceeded previous measures of crustacean grazing in this system. Nonlinear feeding kinetics required that piecewise multiple regression be used to estimate contributions of external, cell quota, and recycling to N and P supply. In deep‐water layers, phytoplankton were growing at nutrient‐saturated rates, indicating that phytoplankton growth was more likely light limited. In the epilimnion, recycled and internal sources were important for both N and P in different experiments, but the importance of various supply sources did not systematically differ for N and P. In epilimnetic experiments, there was strong experiment‐to‐experiment variation in contributions of recycling sources of N and P, suggesting that resupply of N and P via grazers was decoupled. Comparison of phytoplankton responses to nutrient deletion in undiluted vs. highly diluted treatments indicated that inferences regarding frequency and magnitude of nutrient limitation, as well as identity of the primary limiting nutrient, depended on dilution.

Point Estimation of the Parameters of Piecewise Regression Models

Two methods of fitting piecewise multiple regression models are presented. One, based on dynamic programming, yields maximum‐likelihood estimators and is suitable for sequences of moderate length. A second, hierarchical, procedure yields approximations to the maximum‐likelihood estimators and is suitable for very long sequences of data. Both methods have computational requirements that are linear in the number of segments.