Two-way Random Effects Model Research Articles

Nasopharyngeal carcinoma volume measurements determined with computed tomography: study of intraobserver and interobserver variability.

To investigate the intraobserver and interobserver variability of computed tomography-based volume measurements of nasopharyngeal carcinoma. Prospective study. Tertiary care centre. The primary tumour volume of 13 nasopharyngeal carcinomas was repeatedly measured by two trained observers independently in two different sessions, using the summation of area technique. Mean tumour volume and its standard deviation were calculated for each tumour. Statistical analysis was done with multivariate analysis, linear regression, and a two-way analysis of variance (ANOVA) random effects model. The coefficient of variation was less than 20% in 11 volume measurements, but a large discrepancy between observers was noted in two tumours with involvement of the paranasal sinuses. A good linear correlation was found between mean tumour volume and its standard deviation: standard deviation = 0.26 volume - 2.48 (r = .80). When the two tumours with a large coefficient of variation were excluded, the two-way ANOVA random effects model revealed that both the interobserver (p = .83) and the intraobserver (p = .90) effect are not statistically significant; interobserver variability was the major component of total variability (71.0%). Total variability in the computed tomography-based measurement of nasopharyngeal carcinoma volume is small by having the measurements done by a trained observer, except in tumours with involvement of the paranasal sinuses.

A Simple General Method for Constructing Confidence Intervals for Functions of Variance Components

A simple general method is proposed for constructing confidence intervals for arbitrary functions of variance components in balanced normal-theory models. The concept of “surrogate variables” is introduced as part of the description of the method. “Equal-tail” and “shortest-length” confidence intervals from this method can be computed easily using simulations. As an illustration, the two-way random-effects model is considered. It is shown that the proposed method produces intervals that are comparable in confidence coefficient and average length to those produced by the best existing methods.

RELIABILITY OF THE PERONEUS LONGUS, TIBIALIS ANTERIOR AND SOLEUS HOFFMANN REFLEX IN MAN

The reliability of the Hoffmann reflex has been well established in the soleus (Sol) by stimulating posterior tibial nerve in the inferior aspect of the popliteal fossa. Reliability of the peroneus longus (PL), tibialis anterior (TA), and Sol H-reflexes by stimulating both the tibial and common peroneal nerves in the superior angle of the popliteal fossa has not been reported. Therefore, the purpose of this work was to investigate H-reflex intrasession reliability in the PL, TA, and Sol. Twelve young, healthy males and females (age: 22.9 ± 4.9 yrs, height: 172.2 ± 7.9 cm, mass: 75.1 ± 12.1 kg) with no history of lower extremity neurological or orthopedic pathologies within the past year volunteered. A within subjects repeated measures design was used. Measurements were recorded at 0 min (baseline), 5 min, 10 min, 15 min, 20 min, 25 min, 30 min, 35 min, and 40 min. H-reflex data were collected from these muscles via percutaneous stimulation of the tibial and common peroneal nerves in the superior aspect of the popliteal fossa. A high voltage (120–200 V), short duration (1.0 msec) stimulus was delivered, eliciting the H-reflex detected via surface EMG. Five to 12 measurements were taken at 20 sec intervals in order to map the maximum PL, TA, and Sol H-reflexes. All subjects received each trial (PL, TA, Sol) in an order predetermined by a balanced Latin Square. The lowest stimulus intensity necessary to elicit the H-reflex for one of the three muscles was used as the testing stimulus intensity for the course of the study. H-reflex means (five trials) were recorded for the PL, TA, and Sol every five min for 40 min. Intrasession reliability was computed using the two-way random effect model. Interclass Correlation Coefficients were estimated for PL [ICC (2,1) = 0.971], TA [ICC (2,1) = 0.944], and Sol [ICC (2,1) = 0.920] H-reflexes. These data indicated that PL and TA H-reflexes are as reliable as previously reported Sol H-reflexes. Furthermore, the PL, TA, and Sol H-reflexes demonstrate high intrasession reliability when stimulating the tibial and common peroneal nerves in the superior popliteal fossa. Thus, the H-reflex can be used to assess motoneuron pool recruitment following joint injury.

Test-retest reliability study of a new improved Leg-O-meter, the Leg-O-meter II, in patients suffering from venous insufficiency of the lower limbs.

The objective of this study was to evaluate the interobserver and test-retest reliability of the new improved Leg-O-Meter, the Leg-O-Meter II, an instrument designed to measure leg circumference. The new Leg-O-Meter consists of a tape measure fixed to a stand attached to a small board on which the patient is in standing position. Only the left limb is measured. For this study the tape measure of the Leg-O-Meter was fixed at 13 cm from the board. Subjects were recruited from patients consulting the phlebology clinic of Hopital St-Michel, Paris, France. Thirty-nine patients were asked to participate in the test phase and a subsample of 20 patients were asked to participate in addition to a retest phase 10 minutes after their first measurement. Patients were asked to enter a closed room where four independent and blinded observers consecutively took measurements of their left calf with the Leg-O-Meter II. Twenty patients were also asked to come back 10 minutes later for a second round of measurements. While waiting, patients were seated. Variables collected included leg circumference, presence of edema, clinical presentation, and venous insufficiency treatment history. The order of the observers was randomized between patients. Under the assumption of a two-way random effects model, an intraclass correlation coefficient (ICC) was used to determine the reliability of a measure with the Leg-O-Meter II as well as the test-retest reliability. The interobserver and test-retest reliabilities of the Leg-O-Meter II were 98.28% [96.90%, 100.00%] CI95% and 95.90% [92.00%, 100.00%] CI95%, respectively. The Leg-O-Meter II has higher interobserver reliability and is easier to manipulate than the previous version. In addition, it has substantive test-retest reliability.

On the construction of tolerance interval for two-way random effect model

Statistical tolerance limits have been widely applied in the area of applied statistics, particularly in engineering, manufacturing, reliability, and quality control processes in industries. This article attempts to generalize the one-way model into the balanced two-way random effect model and suggest various alternative tolerance limits as a special case of the new complexity. © 2000 John Wiley & Sons, Inc. Complexity 5: 61-64, 2000

On the construction of tolerance interval for two-way random effect model

Statistical tolerance limits have been widely applied in the area of applied statistics, particularly in engineering, manufacturing, reliability, and quality control processes in industries. This article attempts to generalize the one-way model into the balanced two-way random effect model and suggest various alternative tolerance limits as a special case of the new complexity. © 2000 John Wiley & Sons, Inc. Complexity 5: 61-64, 2000

Two-Way Random-Effects Analyses and Gauge R&R Studies

An important prerequisite of any sensible data-based engineering study is the quantification of the precision of gauges or measuring equipment to be used in data collection. It has long been understood that in the event that more than one individual will use a particular gauge, “measurement variation” for that gauge can include not only a kind of “pure error” component but an “operator” or “technician” component as well. Furthermore, it is well known that the two-way random-effects model provides a natural framework for quantifying the different components of measurement variation. Some parts of standard practice in the “gauge R&R studies” aimed at quantifying measurement precision, however, are unfortunately at odds with what makes sense under this model. Thus, the purpose of this primarily expository article is to explain in elementary terms the use of a two-way random-effects model for gauge R&R studies, to critique current practice, and to point out some simple improvements that can follow from more c...

Two-Way Random-Effects Analyses and Gauge R&R Studies

An important prerequisite of any sensible data-based engineering study is the quantification of the precision of gauges or measuring equipment to be used in data collection. It has long been understood that in the event that more than one individual will use a particular gauge, “measurement variation” for that gauge can include not only a kind of “pure error” component but an “operator” or “technician” component as well. Furthermore, it is well known that the two-way random-effects model provides a natural framework for quantifying the different components of measurement variation. Some parts of standard practice in the “gauge R&R studies” aimed at quantifying measurement precision, however, are unfortunately at odds with what makes sense under this model. Thus, the purpose of this primarily expository article is to explain in elementary terms the use of a two-way random-effects model for gauge R&R studies, to critique current practice, and to point out some simple improvements that can follow from more careful attention to the model and well-established practice in the general linear model.

A monotonic property for iterative GLS in the two-way random effects model

Abstract This paper shows that maximum likelihood estimation for the two-way random effects model can be obtained as an iterated GLS procedure based on two subsets of the parameters: The first subset contains the regression coefficients β, and the second subset contains two variance components ratios, θ 1 and θ 2 . Fixing θ i ( i =1, 2) and iterating between β and θ j ( j =1, 2 and j ≠ i ), the sequence of θ j 's generated by this algorithm form a monotonic sequence. This result is an extension of Breusch's (1987) ‘remarkable property’ for iterative GLS from the one-way to the two-way model. Since the θ i 's are both between zero and one, a search over θ i while iterating on the other θ j and β will guard against the possibility of multiple local maxima of the likelihood function. However, such a search procedure can be relatively costly. This paper suggests an alternative computationally more efficient algorithm which makes use of Deaton's (1975) ridge-walking algorithm and Breusch's (1987) monotonic property. The proposed algorithm is shown to converge rapidly for the investment equation considered by Grunfeld (1958).

Round Robin Analysis of Variance via Maximum Likelihood

Abstract A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the EM algorithm is proposed for obtaining the maximum likelihood estimates of the covariance components. A balanced data set is analyzed using the methodology developed.

Round Robin Analysis of Variance Via Maximum Likelihood

Abstract A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the EM algorithm is proposed for obtaining the maximum likelihood estimates of the covariance components. A balanced data set is analyzed using the methodology developed.

A Comparison of the “Sometimes Pool”, “Sometimes Switch” and “Never Pool” Procedures in the Two-Way ANOVA Random Effects Model

In the replicated two-way random-effects model, the “Sometimes Pool” (SP) procedure is employed for the specification of the appropriate model and the subsequent test of the main effects. The “Sometimes Switch” (SW) procedure is introduced and shown to be a limiting form of SP as the cell size increases. This article concerns itself with the question of whether to pool interaction and error mean squares in order to get better tests for the main effects. The significance levels and the powers of the “sometimes” procedures are compared with those of the “Never Pool” (NP). The SP and SW procedures rarely have control over the main test significance level. We recommend modifying the experimental design, when possible, to maximize the interaction degrees of freedom and employing the “Never Pool” procedure.

A Comparison of the "Sometimes Pool", "Sometimes Switch" and "Never Pool" Procedures in the Two-Way ANOVA Random Effects Model

A Comparison of the "Sometimes Pool", "Sometimes Switch" and "Never Pool" Procedures in the Two-Way ANOVA Random Effects Model