Abstract
In scenarios where the variance of a response variable can be attributed to two sources of variation, a confidence interval for a ratio of variance components gives information about the relative importance of the two sources. For example, if measurements taken from different laboratories are nine times more variable than the measurements taken from within the laboratories, then 90% of the variance in the responses is due to the variability amongst the laboratories and 10% of the variance in the responses is due to the variability within the laboratories. Assuming normally distributed sources of variation, confidence intervals for variance components are readily available. In this paper, however, simulation studies are conducted to evaluate the performance of confidence intervals under non-normal distribution assumptions. Confidence intervals based on the pivotal quantity method, fiducial inference, and the large-sample properties of the restricted maximum likelihood (REML) estimator are considered. Simulation results and an empirical example suggest that the REML-based confidence interval is favored over the other two procedures in unbalanced one-way random effects model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3793-3807 |
| Number of pages | 15 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 141 |
| Issue number | 12 |
| DOIs | |
| State | Published - Dec 2011 |
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Keywords
- Fiducial inference
- Pivotal quantity
- Restricted maximum likelihood estimation
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability
Cite this
Confidence intervals for variance components in unbalanced one-way random effects model using non-normal distributions. / Burch, Brent D.
In: Journal of Statistical Planning and Inference, Vol. 141, No. 12, 12.2011, p. 3793-3807.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Confidence intervals for variance components in unbalanced one-way random effects model using non-normal distributions
AU - Burch, Brent D
PY - 2011/12
Y1 - 2011/12
N2 - In scenarios where the variance of a response variable can be attributed to two sources of variation, a confidence interval for a ratio of variance components gives information about the relative importance of the two sources. For example, if measurements taken from different laboratories are nine times more variable than the measurements taken from within the laboratories, then 90% of the variance in the responses is due to the variability amongst the laboratories and 10% of the variance in the responses is due to the variability within the laboratories. Assuming normally distributed sources of variation, confidence intervals for variance components are readily available. In this paper, however, simulation studies are conducted to evaluate the performance of confidence intervals under non-normal distribution assumptions. Confidence intervals based on the pivotal quantity method, fiducial inference, and the large-sample properties of the restricted maximum likelihood (REML) estimator are considered. Simulation results and an empirical example suggest that the REML-based confidence interval is favored over the other two procedures in unbalanced one-way random effects model.
AB - In scenarios where the variance of a response variable can be attributed to two sources of variation, a confidence interval for a ratio of variance components gives information about the relative importance of the two sources. For example, if measurements taken from different laboratories are nine times more variable than the measurements taken from within the laboratories, then 90% of the variance in the responses is due to the variability amongst the laboratories and 10% of the variance in the responses is due to the variability within the laboratories. Assuming normally distributed sources of variation, confidence intervals for variance components are readily available. In this paper, however, simulation studies are conducted to evaluate the performance of confidence intervals under non-normal distribution assumptions. Confidence intervals based on the pivotal quantity method, fiducial inference, and the large-sample properties of the restricted maximum likelihood (REML) estimator are considered. Simulation results and an empirical example suggest that the REML-based confidence interval is favored over the other two procedures in unbalanced one-way random effects model.
KW - Fiducial inference
KW - Pivotal quantity
KW - Restricted maximum likelihood estimation
UR - http://www.scopus.com/inward/record.url?scp=79960841782&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79960841782&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2011.06.015
DO - 10.1016/j.jspi.2011.06.015
M3 - Article
AN - SCOPUS:79960841782
VL - 141
SP - 3793
EP - 3807
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
IS - 12
ER -