We consider the model where φ 1, φ 2 are real coefficients, not necessarily equal, and the at ,'s are a sequence of i.i.d. random variables with mean 0. Necessary and sufficient conditions on the φ 's are given for stationarity of the process. Least squares estimators of the φ 's are derived and, under mild regularity conditions, are shown to be consistent and asymptotically normal. An hypothesis test is given to differentiate between an AR(1) (the case φ 1 = φ 2) and this threshold model. The asymptotic behavior of the test statistic is derived. Small-sample behavior of the estimators and the hypothesis test are studied via simulated data.

Objective We introduce The Psychological Adaptation Scale (PAS) for assessing adaptation to a chronic condition or risk and present validity data from six studies of genetic conditions. Methods Informed by theory, we identified four domains of adaptation: effective coping, self-esteem, social integration, and spiritual/existential meaning. Items were selected from the PROMIS “positive illness impact” item bank and adapted from the Rosenberg self-esteem scale to create a 20-item scale. Each domain included five items, with four sub-scale scores. Data from studies of six populations: adults affected with or at risk for genetic conditions (N=3) and caregivers of children with genetic conditions (N=3) were analyzed using confirmatory factor analyses (CFA). Results CFA suggested that all but five posited items converge on the domains as designed. Invariance of the PAS amongst the studies further suggested it is a valid and reliable tool to facilitate comparisons of adaptation across conditions. Conclusion Use of the PAS will standardize assessments of adaptation and foster understanding of the relationships among related health outcomes, such as quality of life and psychological well-being. Practice Implications Clinical interventions can be designed based on PAS data to enhance dimensions of psychological adaptation to a chronic health condition or risk.

We consider the model where φ1, φ2 are real coefficients, not necessarily equal, and the at,'s are a sequence of i.i.d. random variables with mean 0. Necessary and sufficient conditions on the φ 's are given for stationarity of the process. Least squares estimators of the φ 's are derived and, under mild regularity conditions, are shown to be consistent and asymptotically normal. An hypothesis test is given to differentiate between an AR(1) (the case φ1 = φ2) and this threshold model. The asymptotic behavior of the test statistic is derived. Small-sample behavior of the estimators and the hypothesis test are studied via simulated data.

We consider the model Zt = φ (0, k)+ φ(1, k)Zt–1 + at (k) whenever rk−1<Zt−1≦rk, 1≦k≦l, with r0 = –∞ and rl =∞. Here {φ (i, k); i = 0, 1; 1≦k≦l} is a sequence of real constants, not necessarily equal, and, for 1≦k≦l, {at(k), t≧1} is a sequence of i.i.d. random variables with mean 0 and with {at(k), t≧1} independent of {at(j), t≧1} for j ≠ k. Necessary and sufficient conditions on the constants {φ (i, k)} are given for the stationarity of the process. Least squares estimators of the model parameters are derived and, under mild regularity conditions, are shown to be strongly consistent and asymptotically normal.