On the weak invariance principle for non-adapted stationary random fields under projective criteria

In this paper, we study the central limit theorem (CLT) and its weak invariance principle (WIP) for sums of stationary random fields non-necessarily adapted, under different normalizations. To do so, we first state sufficient conditions for the validity of a suitable ortho-martingale approximation. Then, with the help of this approximation, we derive projective criteria under which the CLT as well as the WIP hold. These projective criteria are in the spirit of Hannan’s condition and are well adapted to linear random fields with ortho-martingale innovations and which exhibit long memory.

Toward a More PERMA(nent) Conceptualization of Worker Well-Being?

We examined the factor structure of the recently developed worker well-being measure Workplace PERMA Profiler and relationships between PERMA dimensions (i.e., positive emotions, engagement, positive relationships, meaning, accomplishment) and job performance (viz., task performance, organizational citizenship behaviors benefiting individuals and the organization at large). The measure exhibited metric (i.e., weak) invariance across samples of participants from the United States ( N = 284) and China ( N = 420). Additionally, for participants who responded to both the Workplace PERMA Profiler and the performance measures, there was a general pattern of positive PERMA–performance relationships across both samples ( NUS = 147; NChina = 202). Overall, the Workplace PERMA Profiler may have problematic psychometric properties and item wordings and thus would benefit from further refinement.

Development of the Perth Adolescent Worry Scale (PAWS)

Tools to assess worry among adolescents exist but do not capture the content of worries. This study reports on the development of a brief, psychometrically sound measure of worry for use with adolescents. Phase 1 involved identification of 27 potential items from existing instruments as well as item generation identified in interviews with students, teachers, school psychologists, and parents. In Phase 2, the candidate items were completed by 835 Australian adolescents (317 males, 508 females, 10 unspecified; Mean age = 13.55, SD = 1.31) from Grades 5 to 10. These data were randomly split in half, and an exploratory factor analysis on the first half identified a two-factor solution with 12 items: Peer Relationships (6 items) and Academic Success and the Future (6 items). On the second half of the data, confirmatory factor analyses supported the factor structure and supported strong invariance across age, socioeconomic status, and presence/absence of a diagnosed neurodevelopmental disorder. Weak invariance was evident across sex. Differences across groups are reported as are correlations with indicators of psychological wellbeing. In conclusion, the Perth Adolescent Worry Scale provides both applied professionals and researchers with a short, easy-to-administer, and psychometrically strong instrument to evaluate adolescents’ everyday worries.

Mixing rates for potentials of non-summable variations

Mixing rates, relaxation rates, and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. This paper exhibits upper bounds for these quantities for dynamics defined by potentials with square-summable variations. We obtain these bounds as corollaries of a new block coupling inequality between pairs of dynamics starting with different histories. As applications of our results, we prove a new weak invariance principle and a Hoeffding-type inequality.

Are growth mindset, mastery orientation, and grit promising for promoting achievement in the Global South? Psychometric evaluations among Indonesian adolescents

We examined the measurement characteristics and cross-cultural measurement invariance of growth mindset, mastery orientation, and grit among Indonesian (N=55,964) and US (N =440) adolescents. We found support for strong invariance across males and females for all factors in both contexts. Indonesian females reported higher growth mindset and mastery orientation latent means than Indonesian males. We found mixed evidence for cross-cultural measurement invariance using two approaches. A Bayesian approach supported measurement invariance for mastery orientation and grit, whereas each factor achieved only configural or weak invariance using subsampling approach based in frequentist estimation. Notably, higher levels of each construct were associated with higher grades in Indonesia and in the US. We conclude that while some measurement issues warrant future investigation, growth mindset, mastery orientation, and grit conceptually translate to the Indonesian context and are promising targets for academic achievement interventions for Indonesian youth and perhaps youth in the broader Global South.

Validity and reliability Measurement of TIMSS 2011 test in mathematics across school location and supervising authority in Jordan: الصدق والثبات في القياس لاختبار تمس (TIMSS 2011) في العلوم للصف الثامن عبر موقع المدرسة والجهة المشرفة في الأردن

The purpose of this study is to examine the measurement invariance of TIMSS mathematics test for eighth grade across school location and the supervising authority (Ministry of Education, UNRWA) in Jordan. To achieve this, the researcher used the analytical descriptive approach to analyze the test results for Jordanian 8th graders who participated in the TIMSS study in 2011. Specifically, the responses of 547 students to 34 items in booklet eight and nine were analyzed. Seven items were excluded because the skewness index is ​​greater than 2 and the kurtosis index is greater than 7. The data of the remaining 27 items were analyzed by using Confirmatory Factor Analysis (CFA) and Multiple Groups Confirmatory Factor Analysis (MGCFA) through the statistical program (AMOS 22). To judge the suitability of the test factorial structure the following goodness-of-fit indices in Structural equation modeling (SEM) were used: Chi Square (χ2) test was a statistically significant value of 468.167 and a good comparison index was CFI statistically significant value of 0.934 which is greater than 0.80 and the square of the mean root error approx. The results showed that there is no Configural invariance according to the location of the school (countryside, city), and the values ​​of the χ2 were a statistical function and its value is 822.858 and a good comparison index CFI is a statistical function and its value is 0.918 which is greater than 0.80 and the mean square root of the approximate error RMSEA is a statistic function and its value is 0.024 which is less than 0.08 and a root index The mean of the standard residual squares of SRMR is statistically significant and its value is 0.0408 which is less than 0.09. The results showed that there is no Metric (or weak) invariance according to the location of the school (countryside, city), the values ​​of the χ2 were a statistical function and its value is 861.321 and a good comparison index CFI is a statistical function and its value is 0.913 which is greater than 0.80 and the average square error of the approximate error RMSEA is a statistical function whose value is 0.024 and is less than 0.08 and an index The root mean standard SRMR squares are 0.0432 and less than 0.09. The results also showed that there was no Scalar (or strong) invariance according to the location of the school (countryside, city), and the values ​​of the χ2 were a statistical function and its value was 910.730 and a good comparison index CFI was a statistical function and its value is 0.903 which is greater than 0.80 and the average square of the approximate error root RMSEA statistically significant value and 0.025 which is less than 0.08 and an index The root mean standard SRMR squared is 0.0430 and is less than 0.09. The results showed that there is no Configural invariance in the supervising authority (Ministry of Education, UNRWA), and the values ​​of the χ2 were a statistically significant value of 833.660 and a good comparison index CFI was a statistical function with a value of 0.898 which is greater than 0.80 and an average square of the root error of approximate RMSEA statistically significant value of 0.028 which is less than 0.08 The mean index of the standard residual squares SRMR is statistically significant, and its value is 0.0351, which is less than 0.09. The results showed that there is no Metric (or weak) invariance for the supervising authority (Ministry of Education, UNRWA), and the values ​​of the χ2 were a statistically significant value of 890.903 and a good comparison index CFI was a statistically significant value of 0.883 which is greater than 0.80 and the square of the mean root error of approx. RMSEA statistically significant value of 0.029 which is less than 0.08 and the mean root index of the standard residual squares SRMR are statistically significant and have a value of 0.0620 which is less than 0.09. The results also showed that there is no Scalar (or strong) invariance of the supervising authority (Ministry of Education, UNRWA), and the values ​​of the χ2 were a statistical function and its value is 993.653 and a good comparison index CFI is a statistical function and its value is 0.854 and it is greater than 0.80 and the square of the average root error of RMSEA is a statistic function and its value is 0.033 which is less than 0.08 and the mean root index of the standard SRMR squares are statistically significant and their value is 0.0634 which is less than 0.09.

Stationary Sequences in a Random Time Scenery

In this chapter, we analyze the asymptotic behavior of the partial sums process associated with examples of stationary sequences in a random time scenery. The examples considered are stationary sequences sampled by shifted renewal Markov chains and random walks in a strictly stationary scenery. The asymptotic behavior of the partial sums process is essentially investigated with the help of the weak invariance principles stated in Chapter 4. More precisely, for the partial sums process associated with a stationary process sampled by a renewal Markov chain stated at zero, due to the non-stationarity of the underlying sequence, the functional CLT is obtained as an application of the functional CLT for non-stationary sequences developed in Section 4.4. In the case where we are sampling a strictly stationary random scenery by a random walk, stationarity is preserved, and the invariance principle is then derived by using the functional CLT under Maxwell–Woodroofe condition.