scholarly journals Missing observations: The loss in relative A-, D- and G-efficiency

2017 ◽  
Vol 5 (2) ◽  
pp. 43
Author(s):  
Mary Iwundu
Keyword(s):  
Relative Efficiency ◽  
Missing Observations ◽  
Design Efficiency ◽  
Response Models ◽  
Vertex Point ◽  
Multiple Observations ◽  
Percentage Loss ◽  
Center Point ◽  
Negative Effect

The loss in Relative A-, D- and G-efficiency due to missing single or multiple observations is studied using cuboidal designs associated with response models. Higher losses in Relative A- and D-efficiencies are attributed to missing vertex points. The absence of one or two center points does not affect any of Relative A-, D- and G-efficiency, but when its absence is in combination with either a vertex or axial point, there is some negative effect on the design efficiency resulting in some percentage loss in Relative efficiency. The loss in relative efficiency is higher when the missing center point is in combination with missing vertex point. Losses in Relative A- and D-efficiencies are generally higher than losses in Relative G-efficiency. In fact, Relative G-efficiency is mildly affected by the missing vertex or axial point or both.

scholarly journals Construction of Modified Central Composite Designs for Non-standard Models

2018 ◽  
Vol 7 (5) ◽  
pp. 95
Author(s):  
Iwundu, M. P.
Keyword(s):  
Loss Function ◽  
Information Matrix ◽  
Missing Observations ◽  
Design Efficiency ◽  
Central Composite Designs ◽  
Standard Models ◽  
Alternative Designs ◽  
Composite Designs ◽  
Hat Matrix ◽  
Central Composite

The use of loss function in studying the reduction in determinant of information matrix due to missing observations has effectively produced designs that are robust to missing observations. Modified central composite designs are constructed for non-standard models using principles of the loss function or equivalently first compound of (I ) matrix associated with hat matrix . Although central composite designs (CCDs) are reasonably robust to model mis-specifications, efficient designs with fewer design points are more economical. By classifying the losses due to missing design points in the CCD portions, where there are multiple losses associated with specified CCD portions, the design points having less influence may be deleted from the full CCD. This leads to a possible increase in design efficiency and offers alternative designs, similar in the structure of CCDs, for non-standard models.

scholarly journals Missing Observations in Split-Plot Central Composite Designs: The Loss in Relative A-, G-, and V- Efficiency

2021 ◽  
Vol 25 (2) ◽  
pp. 239-247
Author(s):  
Y. Yakubu ◽  
A.U. Chukwu
Keyword(s):  
Model Parameters ◽  
Missing Observations ◽  
Prediction Variance ◽  
Efficiency Losses ◽  
Split Plot ◽  
Negative Effect ◽  
Central Composite Designs ◽  
Plot Structure ◽  
Composite Designs ◽  
Central Composite

The trace (A), maximum average prediction variance (G), and integrated average prediction variance (V) criteria are experimental design evaluation criteria, which are based on precision of estimates of parameters and responses. Central Composite Designs(CCD) conducted within a split-plot structure (split-plot CCDs) consists of factorial (𝑓), whole-plot axial (𝛼), subplot axial (𝛽), and center (𝑐) points, each of which play different role in model estimation. This work studies relative A-, G- and V-efficiency losses due to missing pairs of observations in split-plot CCDs under different ratios (d) of whole-plot and sub-plot error variances. Three candidate designs of different sizes were considered and for each of the criteria, relative efficiency functions were formulated and used to investigate the efficiency of each of the designs when some observations were missing relative to the full one. Maximum A-efficiency losses of 19.1, 10.6, and 15.7% were observed at 𝑑 = 0.5, due to missing pairs 𝑓𝑓, 𝛽𝛽, and 𝑓𝛽, respectively, indicating a negative effect on the precision of estimates of model parameters of these designs. However, missing observations of the pairs- 𝑐𝑐, 𝛼𝛼, 𝛼𝑐, 𝑓𝑐, and 𝑓𝛼 did not exhibit any negative effect on these designs' relative A-efficiency. Maximum G- and Vefficiency losses of 10.1,16.1,0.1% and 0.1, 1.1, 0.2%, were observed, respectively, at 𝑑 = 0.5, when the pairs- 𝑓𝑓, 𝛽𝛽, 𝑐𝑐, were missing, indicating a significant increase in the designs' maximum and average variances of prediction. In all, the efficiency losses become insignificant as d increases. Thus, the study has identified the positive impact of correlated observations on efficiency of experimental designs. Keywords: Missing Observations, Efficiency Loss, Prediction variance

A Theory of Higher Order Interactions Between Sensitive Variables: Empirical Evidences and an Application to a Variety of Smoking

2021 ◽  
pp. 004912412098620
Author(s):  
Oluwaseun L. Olanipekun ◽  
JuLong Zhao ◽  
Rongdong Wang ◽  
Stephen A.Sedory ◽  
Sarjinder Singh
Keyword(s):  
Simple Model ◽  
Privacy Protection ◽  
Relative Efficiency ◽  
Higher Order ◽  
Randomized Response ◽  
Response Models ◽  
Unbiased Estimators ◽  
Sensitive Characteristics ◽  
Randomized Response Models ◽  
Theoretical Results

In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing sensitive characteristics. However, there is a paucity of research studies that have addressed higher order interactions between these sensitive characters. In this article, we develop a new theory based on three proposed randomized response models which we name as: simple model, semi-crossed model, and fully crossed model. Twenty-one new unbiased estimators of seven parameters are introduced, their variance expressions are derived, and unbiased estimators of variances are developed. The three models are compared under various values of the parameters by computing the percent relative efficiency of one model over another model. The most efficient model is then applied to study the population proportions of three varieties of smoking habits among students, and their first- and second-order interactions. The last four sections (Ninth to Twelfth) are verifications of theoretical results using the Cramer–Rao lower bounds of variances for the developed 21 new estimators in randomized response sampling.

Social Motives Predict Loneliness During a Developmental Transition

2017 ◽  
Vol 76 (4) ◽  
pp. 145-153 ◽  
Author(s):  
Jana Nikitin ◽  
Alexandra M. Freund
Keyword(s):  
Social Relationships ◽  
Well Being ◽  
Social Avoidance ◽  
Social Approach ◽  
Social Motives ◽  
Developmental Transitions ◽  
Avoidance Motivation ◽  
Negative Effect ◽  
Low Levels

Abstract. Establishing new social relationships is important for mastering developmental transitions in young adulthood. In a 2-year longitudinal study with four measurement occasions (T1: n = 245, T2: n = 96, T3: n = 103, T4: n = 85), we investigated the role of social motives in college students’ mastery of the transition of moving out of the parental home, using loneliness as an indicator of poor adjustment to the transition. Students with strong social approach motivation reported stable and low levels of loneliness. In contrast, students with strong social avoidance motivation reported high levels of loneliness. However, this effect dissipated relatively quickly as most of the young adults adapted to the transition over a period of several weeks. The present study also provides evidence for an interaction between social approach and social avoidance motives: Social approach motives buffered the negative effect on social well-being of social avoidance motives. These results illustrate the importance of social approach and social avoidance motives and their interplay during developmental transitions.

A Longitudinal Study of Mental Health in Emerging Adults

2014 ◽  
Vol 73 (3) ◽  
pp. 135-141 ◽  
Author(s):  
Monica S. Bachmann ◽  
Hansjörg Znoj ◽  
Katja Haemmerli
Keyword(s):  
Mental Health ◽  
Longitudinal Study ◽  
Emerging Adults ◽  
Poor Mental Health ◽  
Need Satisfaction ◽  
Computer Assisted ◽  
Consistency Model ◽  
Negative Effect ◽  
The Cross ◽  
Health Model

Emerging adulthood is a time of instability. This longitudinal study investigated the relationship between mental health and need satisfaction among emerging adults over a period of five years and focused on gender-specific differences. Two possible causal models were examined: (1) the mental health model, which predicts that incongruence is due to the presence of impaired mental health at an earlier point in time; (2) the consistency model, which predicts that impaired mental health is due to a higher level of incongruence reported at an earlier point in time. Emerging adults (N = 1,017) aged 18–24 completed computer-assisted telephone interviews in 2003 (T1), 2005 (T2), and 2008 (T3). The results indicate that better mental health at T1 predicts a lower level of incongruence two years later (T2), when prior level of incongruence is controlled for. The same cross-lagged effect is shown for T3. However, the cross-lagged paths from incongruence to mental health are marginally associated when prior mental health is controlled for. No gender differences were found in the cross-lagged model. The results support the mental health model and show that incongruence does not have a long-lasting negative effect on mental health. The results highlight the importance of identifying emerging adults with poor mental health early to provide support regarding need satisfaction.

Working Memory, Mental Prospection, Time Orientation, and Cognitive Insight

2013 ◽  
Vol 34 (3) ◽  
pp. 159-169 ◽  
Author(s):  
Sevtap Cinan ◽  
Aslı Doğan
Keyword(s):  
Working Memory ◽  
Structural Equation ◽  
Factor Model ◽  
Time Orientation ◽  
Equation Modeling ◽  
Cognitive Insight ◽  
Confirmatory Factor ◽  
Negative Effect ◽  
Positive Effect ◽  
Three Factor

This research is new in its attempt to take future time orientation, morningness orientation, and prospective memory as measures of mental prospection, and to examine a three-factor model that assumes working memory, mental prospection, and cognitive insight are independent but related higher-order cognitive constructs by using confirmatory factor analysis (CFA). The three-factor model produced a good fit to the data. An alternative one-factor model was tested and rejected. The results suggest that working memory and cognitive insight are distinguishable, related constructs, and that both are distinct from, but negatively associated with, mental prospection. In addition, structural equation modeling (SEM) showed that working memory had a strong positive effect on cognitive insight and a moderate negative effect on mental prospection.

The Multilevel p2 Model

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 42-47 ◽  
Author(s):  
Bonne J. H. Zijlstra ◽  
Marijtje A. J. van Duijn ◽  
Tom A. B. Snijders
Keyword(s):  
Social Network ◽  
Network Data ◽  
Mcmc Algorithm ◽  
Independent Observation ◽  
Single Observation ◽  
Multiple Networks ◽  
Social Network Data ◽  
Multiple Observations ◽  
Practical Support ◽  
The Social

The p 2 model is a random effects model with covariates for the analysis of binary directed social network data coming from a single observation of a social network. Here, a multilevel variant of the p 2 model is proposed for the case of multiple observations of social networks, for example, in a sample of schools. The multilevel p 2 model defines an identical p 2 model for each independent observation of the social network, where parameters are allowed to vary across the multiple networks. The multilevel p 2 model is estimated with a Bayesian Markov Chain Monte Carlo (MCMC) algorithm that was implemented in free software for the statistical analysis of complete social network data, called StOCNET. The new model is illustrated with a study on the received practical support by Dutch high school pupils of different ethnic backgrounds.

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