{"id":81962,"date":"2019-01-30T12:13:47","date_gmt":"2019-01-30T17:13:47","guid":{"rendered":"https:\/\/mrnf.gouv.qc.ca\/nos-publications\/variance-covariance-structure\/"},"modified":"2019-01-30T12:13:47","modified_gmt":"2019-01-30T17:13:47","slug":"variance-covariance-structure","status":"publish","type":"cpt_publication","link":"https:\/\/mrnf.gouv.qc.ca\/en\/our-publications\/variance-covariance-structure\/","title":{"rendered":"A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling"},"content":{"rendered":"\n<p>Published in <strong>European Journal of Forest Research 126: 573-585<\/strong><\/p>\n<p>This study proposes a within-subject variance-covariance (VC) structure to take into account repeated measurements and heteroscedasticity in a context of growth modeling. The VC structure integrates a variance function and a continuous autoregressive covariance structure. It was tested on a nonlinear growth model parameterized with data from permanent sample plots. Using a stand-level approach, basal area growth was independently modeled for red spruce (<em>Picea rubens<\/em> Sarg.) and balsam fir [<em>Abies balsamea<\/em> (L.) Mill.] in mixed stands. For both species, the implementation of the VC structure significantly improved the maximum likelihood of the model. In both cases, it efficiently accounted for heteroscedasticity and autocorrelation, since the normalized residuals no longer exhibited departures from the assumptions of independent error terms with homegeneous variances. Moreover, compared with traditional nonlinear least sqares (NLS) models, models parameterized with this VC structure may generate more accurate predictions when prior information is available. This case study demonstrates that the implementation of a VC structure may provide parameter estimates that are consistent with asymptotically unbiased variances in a context of nonlinear growth modeling using a stand-level approach. Since the variances are no longer biased, the hypothesis tests performed on the estimates are valid when the number of observations is large.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Published in European Journal of Forest Research 126: 573-585 This study proposes a within-subject variance-covariance (VC) structure to take into account repeated measurements and heteroscedasticity in a context of growth modeling. The VC structure integrates a variance function and a continuous autoregressive covariance structure. It was tested on a nonlinear growth model parameterized with data [&hellip;]<\/p>\n","protected":false},"template":"","format":"standard","cptt_secteur":[1179],"cptt_theme":[1180,1181,1182],"cptt_categ_publi":[1149],"cptt_auteurs_ministeriels":[],"class_list":["post-81962","cpt_publication","type-cpt_publication","status-publish","format-standard","hentry","cptt_secteur-forests","cptt_theme-forestry-research","cptt_theme-forests","cptt_theme-silviculture","cptt_categ_publi-scientific-article"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling - Minist\u00e8re des Ressources naturelles et des For\u00eats<\/title>\n<meta name=\"description\" content=\"This study proposes a within-subject variance-covariance structure to take into account repeated measurements and heteroscedasticity\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mrnf.gouv.qc.ca\/en\/our-publications\/variance-covariance-structure\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling - 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