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Articles containing the keyword 'mixed model'.

Category: Research article

article id 10055, category Research article
Jaakko Repola, Hannu Hökkä, Hannu Salminen. (2018). Models for diameter and height growth of Scots pine, Norway spruce and pubescent birch in drained peatland sites in Finland. Silva Fennica vol. 52 no. 5 article id 10055. https://doi.org/10.14214/sf.10055
Highlights: Tree growth strongly correlated with site drainage status; Between-tree competition had a higher impact on tree diameter growth than on height growth; Growth predicted by the constructed models were calibrated using NFI11 data to ensure generally applicable growth predictions level in whole country.

The aim of this study was to develop individual-tree diameter and height growth models for Scots pine, Norway spruce, and pubescent birch growing in drained peatlands in Finland. Trees growing in peatland sites have growth patterns that deviate from that of trees growing in mineral soil sites. Five-year growth was explained by tree diameter, different tree and stand level competition measures, management operations and site characteristics. The drainage status of the site was influencing growth directly or in interaction with other variables. Site quality had a direct impact but was also commonly related to current site drainage status (need for ditch maintenance). Recent thinning increased growth of all species and former PK fertilization increased growth of pine and birch. Temperature sum was a significant predictor in all models and altitude for spruce and birch. The data were a subsample of the 7th National Forest Inventory (NFI) sample plots representing northern and southern Finland and followed by repeated measurements for 15–20 yrs. Growth levels predicted by the models were calibrated using NFI11 data to remove bias originating from the sample of the modelling data. The mixed linear models technique was used in model estimation. The models will be incorporated into the MOTTI stand simulator to replace the current peatlands growth models.

  • Repola, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail: jaakko.repola@luke.fi (email)
  • Hökkä, Natural Resources Institute Finland (Luke), Natural resources, Paavo Havaksen tie 3, FI-90014 University OF Oulu, Finland ORCID ID:E-mail: hannu.hokka@luke.fi
  • Salminen, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail: hannu.salminen@luke.fi
article id 9933, category Research article
Timo Saksa, Jari Miina, Hilkka Haatainen, Kauko Kärkkäinen. (2018). Quality of spot mounding performed by continuously advancing mounders. Silva Fennica vol. 52 no. 2 article id 9933. https://doi.org/10.14214/sf.9933
Highlights: The number and quality of mounds varied considerably according to the operating conditions;The main factors reducing the quality of spot mounding were steep terrain, a thick humus layer, fresh logging residues, stoniness and soil texture;With careful selection of timing and conditions for mounding, the quality obtained by continuously advancing mounders can be improved.

Operating conditions affecting the quality of spot mounding by Bracke continuously advancing mounders were investigated on 66 regeneration areas (124 ha) in eastern Finland. The quality of mounds was classified as suitable (good or acceptable after additional compression) or unsuitable for planting. Models were constructed for the number of suitable planting spots obtained per hectare (good and acceptable mounds), the probability of successful mounding (≥1600 planting spots ha–1) and the probability of creating a suitable mound as a function of terrain, site and soil characteristics, as well as slash conditions (removed, fresh or dry logging residues). The average number of mounds created was 1892 ± 290 mounds ha–1, of which 1398 ± 325 mounds ha–1 (74%) were classified as suitable for planting. The quality of spot mounding was reduced by steep terrain, a thick humus layer and fresh logging residues. Stoniness and soil texture also affected the number of planting spots created. Mounding after logging residues had dried increased the number of planting spots by 191 spots ha–1 compared with mounding in the presence of fresh residues. Removing residues did not significantly increase the number of planting spots compared with mounding amongst dry residues. A thick humus layer, very stony soil, steep slopes and valley terrain decreased the number of planting spots by 150–450 spots ha–1. The number and quality of mounds varied considerably according to the operating conditions, but with careful selection of timing and sites the quality obtained by a continuously advancing mounder can be improved.

  • Saksa, Natural Resources Institute Finland (Luke), Juntintie 154, FI-77600 Suonenjoki, Finland ORCID ID:E-mail: timo.saksa@luke.fi (email)
  • Miina, Natural Resources Institute Finland (Luke), Yliopistokatu 6, FI-80100 Joensuu, Finland ORCID ID:E-mail: jari.miina@luke.fi
  • Haatainen, Faculty of Science and Forestry, School of Forest Sciences, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: hilkka.haatainen@storaenso.com
  • Kärkkäinen, Tornator Oyj, Muuntamontie 2, FI-80100 Joensuu, Finland ORCID ID:E-mail: kauko.karkkainen@tornator.fi
article id 1342, category Research article
Blas Mola-Yudego, Gianni Picchi, Dominik Röser, Raffaele Spinelli. (2015). Assessing chipper productivity and operator effects in forest biomass operations. Silva Fennica vol. 49 no. 5 article id 1342. https://doi.org/10.14214/sf.1342
Highlights: A model is constructed to assess the productivity in chipping of wood biomass at roadside; The data includes 172 trials and 67 operators in Italy; The operator effect was included in a mixed model approach; The R2 were 0.76 (fixed part) and 0.88 (incl. operator effects).

The present research focuses on the productivity of energy wood chipping operations at several sites in Italy. The aim was to assess the productivity and specifically the effect attributed to the operator in the chipping of wood biomass. The research included 172 trials involving 67 operators across the country that were analysed using a mixed model approach, in order to assess productivity, and to isolate the operator effect from other potential variables. The model was constructed using different predictors aiming to explain the variability due to the machines and the raw-materials. The final model included the average piece weight of raw material chipped as well as the power of the machine. The coefficients of determination (R2) were 0.76 for the fixed part of the model, and 0.88 when the effects due to the operators were included. The operators’ performance compared to their peers was established, and it was compared to a subjective classification based on the operator’s previous experience. The results of this study can help to the planning and logistics of raw material supply for bioenergy, as well as to a more effective training of future forest operators.

  • Mola-Yudego, School of Forest Sciences, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland; NIBIO Norwegian Institute of Bioeconomy Research, P.O. Box 115, 1431 Ås, Norway ORCID ID: http://orcid.org/0000-0003-0286-0170 E-mail: blas.mola@uef.fi (email)
  • Picchi, CNR IVALSA, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy ORCID ID:E-mail: picchi@ivalsa.cnr.it
  • Röser, Forest Feedstocks Group, FPInnovations, Vancouver, British Columbia, Canada ORCID ID:E-mail: dominik.roser@fpinnovations.ca
  • Spinelli, CNR IVALSA, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy ORCID ID:E-mail: spinelli@ivalsa.cnr.it
article id 1005, category Research article
Marjut Turtiainen, Jari Miina, Kauko Salo, Juha-Pekka Hotanen. (2013). Empirical prediction models for the coverage and yields of cowberry in Finland. Silva Fennica vol. 47 no. 3 article id 1005. https://doi.org/10.14214/sf.1005
Highlights: The site fertility significantly affected the abundance of cowberry on mineral soils, spruce mires and pine mires; The stand basal area and dominant tree species were among the most important forest structural predictors in the model for the coverage; In the cowberry yield model developed for mineral soil sites, the stand basal area and coverage of cowberry plants were statistically significant predictors.
Empirical models for the coverage and berry yield of cowberry (Vaccinium vitis-idaea L.) were developed using generalized linear mixed models (GLMMs). The percentage coverage of cowberry was predicted as a function of site and stand characteristics using data from the Finnish National Forest Inventory (NFI) in 1995. The average annual yield, including the between-year variation in the yield, was predicted as a function of percentage coverage and stand characteristics using permanent experimental plots (MASI) established in different areas of Finland and measured in 2001-2012. The model for cowberry yields (Model 2) was developed for mineral soil forests. The model for the coverage (Model 1) was constructed so that it considers both mineral soil sites and also many other sites where cowberry occurs in the field layer. According to Model 1, the site fertility significantly affected the abundance of cowberry on mineral soils, spruce mires and pine mires. The stand basal area and dominant tree species were among the most important forest structural predictors in Model 1. The site fertility was not a significant predictor in the cowberry yield model. Instead, the stand basal area and coverage of cowberry plants were found to be statistically significant predictors in Model 2. The estimated models were used to predict the cowberry coverage, average annual yield and its 95 % confidence interval along with stand development. The models of this study can be used for multi-objective forest planning purposes.
  • Turtiainen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: marjut.turtiainen@uef.fi (email)
  • Miina, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: jari.miina@metla.fi
  • Salo, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: kauko.salo@metla.fi
  • Hotanen, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: juha-pekka.hotanen@metla.fi
article id 131, category Research article
Timo Pukkala, Tatu Hokkanen, Teijo Nikkanen. (2010). Prediction models for the annual seed crop of Norway spruce and Scots pine in Finland. Silva Fennica vol. 44 no. 4 article id 131. https://doi.org/10.14214/sf.131
Many studies indicate that the flowering abundance of boreal trees strongly correlates with the weather conditions of the previous summer. This study developed prediction models for the seed crops of Norway spruce and Scots pine using weather variables one and two years prior to flowering year as predictors. Weather data, systematically recorded at many weather stations, were obtained from the Finnish Meteorological Institute. Seed crop monitoring data came from 22 spruce stands and 44 pine stands. In every stand, seed crop has been monitored for many years, the longest continuous period being 45 years. Monthly mean temperatures, monthly rainfalls, and periodical temperature sums were used as predictors in the seed crop models. Generally, both tree species flowered abundantly one year after a warm summer and two years after a cool summer. While the models only explained about 45% of the variation in the annual seed crop, they accurately predicted good and bad seed years: when the models predicted good seed crops the likelihood to have at least a medium seed crop was very high and when the models predicted small seed crops, the likelihood to obtain medium or good seed crop was very low. Therefore, the models reliably predict if a particular year will be a good seed year or a poor seed year. These predictions can be used in forestry practice for proper timing of natural regeneration activities, and when activities in seed orchards are planned.
  • Pukkala, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: timo.pukkala@uef.fi (email)
  • Hokkanen, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland ORCID ID:E-mail:
  • Nikkanen, Finnish Forest Research Institute, Finlandiantie 18, FI-58450 Punkaharju, Finland ORCID ID:E-mail:
article id 181, category Research article
Jari Miina, Juha-Pekka Hotanen, Kauko Salo. (2009). Modelling the abundance and temporal variation in the production of bilberry (Vaccinium myrtillus L.) in Finnish mineral soil forests. Silva Fennica vol. 43 no. 4 article id 181. https://doi.org/10.14214/sf.181
Empirical models for the abundance and berry yield of V. myrtillus were constructed using generalized linear mixed model (GLMM) techniques. The percentage coverage of bilberry was predicted as a function of site and stand characteristics using the permanent sample plots of the National Forest Inventory (NFI) in 1995. The number of bilberries was predicted as a function of percentage coverage and stand characteristics using a sub-sample of the NFI plots in North Karelia. The between-year variation in the bilberry yield was analysed using the permanent experimental plots (MASI) established in different areas of Finland and measured in 2001–2007. The highest coverage of bilberry was found on mesic heath sites; on sub-xeric and herb-rich heath sites the values were 62% of that for mesic sites. The decreasing effect of deciduous trees (compared to spruce) was significant only on herb-rich heath sites. The coverage increased along with stand development up to certain stand ages and basal areas. The bilberry yields were higher in pine-dominated stands than in spruce-dominated ones. In spruce stands, the coverage of bilberry and stand basal area significantly affected the number of berries, whereas in pine stands only the coverage was a significant predictor. In the MASI data, the bilberry yield of pine stands was two times higher than that of spruce stands; however, the between-year variation in bilberry yield was higher in the spruce than in the pine stands. The estimated models were used to predict the bilberry coverage and yield along with stand development. On mesic heath sites in southern Finland (1200 dd.), the predicted annual yield of bilberry was about 25 kg ha–1 (95% confidence interval 9–73 kg ha–1) in a mature pine stand and about 10 kg ha–1 (3–35 kg ha–1) in a mature spruce stand. The models can be included in stand simulators, where they would facilitate the prediction of bilberry abundance and yields for silvicultural and forest planning purposes.
  • Miina, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: jari.miina@metla.fi (email)
  • Hotanen, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Salo, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail:
article id 322, category Research article
Jaakko Repola. (2006). Models for vertical wood density of Scots pine, Norway spruce and birch stems, and their application to determine average wood density. Silva Fennica vol. 40 no. 4 article id 322. https://doi.org/10.14214/sf.322
The purpose of this study was to investigate the vertical dependence of the basic density of Scots pine, Norway spruce, and birch stems, and how such dependence could be applied for determining the average stem wood density. The study material consisted of 38 Scots pine (Pinus sylvestris), 39 Norway spruce (Picea abies [L.] Karst.) and 15 birch (Betula pendula and Betula pubescens) stands located on mineral soil sites in southern Finland. The stem material mainly represented thinning removal from stands at different stages of development. The linear mixed model technique, with both fixed and random effects, was used to estimate the model. According to the fixed part of the model, wood density was dependent on the vertical location along the stem in all three tree species. Wood density in pine decreased from the butt to the top, and the gradient in wood density was steep at the butt but decreased in the upper part of the stem. The vertical dependence was similar in birch, but the density gradient was much smaller. For spruce the vertical dependence of the basic density was moderate. The model can be calibrated for a tree stem when one or more sample disks are measured at freely selected heights. Using treewise calibrated predictions of the vertical density dependence and measured stem diameters, almost unbiased estimates, and lower prediction errors than with traditional methods, were obtained for the average stem wood density. The advantages of the method were greater for pine with a strong vertical dependence in basic density, than for spruce and birch.
  • Repola, Finnish Forest Research Institute, Rovaniemi Research Unit, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail: jaakko.repola@metla.fi (email)
article id 395, category Research article
Lauri Mehtätalo. (2005). Height-diameter models for Scots pine and birch in Finland. Silva Fennica vol. 39 no. 1 article id 395. https://doi.org/10.14214/sf.395
Height-Diameter (H-D) models for two shade-intolerant tree species were estimated from longitudinal data. The longitudinal character of the data was taken into account by estimating the models as random effects models using two nested levels: stand and measurement occasion level. The results show that the parameters of the H-D equation develop over time but the development rate varies between stands. Therefore the development of the parameters is not linked to the stand age but to the median diameter of the basal-area weighted diameter distribution (DGM). Models were estimated with different predictor combinations in order to produce appropriate models for different situations. The estimated models can be localized for a new stand using measured heights and diameters, presumably from different points in time, and the H-D curves can be projected into the future.
  • Mehtätalo, Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: lauri.mehtatalo@metla.fi (email)
article id 394, category Research article
Rafael Calama, Gregorio Montero. (2005). Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach. Silva Fennica vol. 39 no. 1 article id 394. https://doi.org/10.14214/sf.394
Diameter increment for stone pine (Pinus pinea L.) is described using a multilevel linear mixed model, where stochastic variability is broken down among period, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, dominant height or site index are included in the model as fixed effects in order to explain residual random variability. The effect of competition on diameter increment is expressed by including distance independent competition indices. The entrance of regional effects within the model is tested to determine whether a single model is sufficient to explain stone pine diameter increment in Spain, or if, on the contrary, regional models are needed. Diameter increment model can be calibrated by predicting random components using data from past growth measurements taken in a complementary sample of trees. Calibration is carried out by using the best linear unbiased predictor (BLUP) theory. Both the fixed effects model and the calibrated model mean a substantial improvement when compared with the classical approach, widely used in forest management, of assuming constancy in diameter increment for a short projection period.
  • Calama, CIFOR-INIA, Grupo Selvicultura Mediterranea, Apdo. 8111, 28080 Madrid, Spain ORCID ID:E-mail: rcalama@inia.es (email)
  • Montero, CIFOR-INIA, Grupo Selvicultura Mediterranea, Apdo. 8111, 28080 Madrid, Spain ORCID ID:E-mail:
article id 504, category Research article
Sylvain Jutras, Hannu Hökkä, Virpi Alenius, Hannu Salminen. (2003). Modeling mortality of individual trees in drained peatland sites in Finland. Silva Fennica vol. 37 no. 2 article id 504. https://doi.org/10.14214/sf.504
Multilevel logistic regression models were constructed to predict the 5-year mortality of Scots pine (Pinus sylvestris L.) and pubescent birch (Betula pubescens Ehrh.) growing in drained peatland stands in northern and central Finland. Data concerning tree mortality were obtained from two successive measurements of the National Forest Inventory-based permanent sample plot data base covering pure and mixed stands of Scots pine and pubescent birch. In the modeling data, Scots pine showed an average observed mortality of 2.73% compared to 2.98% for pubescent birch. In the model construction, stepwise logistic regression and multilevel models methods were applied, the latter making it possible to address the hierarchical data, thus obtaining unbiased estimates for model parameters. For both species, mortality was explained by tree size, competitive position, stand density, species admixture, and site quality. The expected need for ditch network maintenance or re-paludification did not influence mortality. The multilevel models showed the lowest bias in the modeling data. The models were further validated against independent test data and by embedding them in a stand simulator. In 100-year simulations with different initial stand conditions, the models resulted in a 72% and 66% higher total mortality rate for the stem numbers of pine and birch, respectively, compared to previously used mortality models. The developed models are expected to improve the accuracy of stand forecasts in drained peatland sites.
  • Jutras, Département des sciences du bois et de la forêt, Université Laval, Ste-Foy, Québec, G1K 7P4, Canada ORCID ID:E-mail:
  • Hökkä, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN 96301 Rovaniemi, Finland ORCID ID:E-mail: hannu.hokka@metla.fi (email)
  • Alenius, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN 96301 Rovaniemi, Finland ORCID ID:E-mail:
  • Salminen, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN 96301 Rovaniemi, Finland ORCID ID:E-mail:
article id 513, category Research article
Marjut Ihalainen, Kauko Salo, Timo Pukkala. (2003). Empirical prediction models for Vaccinium myrtillus and V. vitis-idaea berry yields in North Karelia, Finland. Silva Fennica vol. 37 no. 1 article id 513. https://doi.org/10.14214/sf.513
Forest berries and the outdoor experiences related to berry collection are important goods and services provided by Finnish forests. Consequently, there is a need for models which facilitate the prediction of the impacts of alternative forest management options on berry yields. Very few such models are available. In particular, empirical models are lacking. Models used in forest management should express the effect of variables altered in forest management such as stand density and mean tree size. This study developed empirical models for bilberry and cowberry yields in North Karelia. The data consisted of 362 measurements of 40 m2 sample plots. The plots were located in clusters. The same plot was measured over 1 to 4 years. Besides berry yield some site and growing stock characteristics of each plot were measured. A random parameter model was used to express the berry yield as a function of site fertility, growing stock characteristics, and random parameters. The random part of the models accounted for the effect of plot, measurement year, and cluster. The fixed predictors of the model for bilberry were stand age and forest site type. Stand basal area, mean tree diameter and forest site type were used to predict cowberry yields. The most significant random parameter was the plot factor. The fixed model part explained only a few per cent of the variation in berry yields. The signs of regression coefficients were logical and the model predictions correlated rather well with the predictions of earlier models.
  • Ihalainen, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland ORCID ID:E-mail: marjut.ihalainen@joensuu.fi (email)
  • Salo, The Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FIN-80101 Joensuu, Finland ORCID ID:E-mail:
  • Pukkala, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland ORCID ID:E-mail:

Category: Research note

article id 1573, category Research note
Marjut Turtiainen, Jari Miina, Kauko Salo, Juha-Pekka Hotanen. (2016). Modelling the coverage and annual variation in bilberry yield in Finland. Silva Fennica vol. 50 no. 4 article id 1573. https://doi.org/10.14214/sf.1573
Highlights: The highest bilberry coverage was found in mesic heath forests and fell forests; On peatlands the coverage was, on average, lower than on mineral soil sites; The approach introduced in this study to calculating annual berry yield indices is a promising way for estimating total annual bilberry yields over a given period of time.

The coverage of bilberry (Vaccinium myrtillus L.) was modelled as a function of site and stand characteristics using the permanent sample plots of the National Forest Inventory (NFI) (Model 1). The sample sites consisted of mineral soil forests as well as fells and peatland sites. Annual variation in the bilberry yield (Model 2) was analysed based on measurements over 2001–2014 in the permanent sample plots (so-called MASI plots) in various areas of Finland. We derived annual bilberry yield indices from the year effects of Model 2 and investigated whether these indices could be used to estimate annual variation in bilberry crops in Finland. The highest bilberry coverage was found in mesic heath forests and fell forests. On peatlands the coverage was, on average, lower than on mineral soil sites; the peatland sites with most bilberry coverage were meso-oligotrophic and oligotrophic spruce mires and oligotrophic pine mires. Our bilberry yield indices showed similar variation to those derived from the mean annual berry yields reported and calculated earlier using the MASI plots; the correlation between the indices was 0.795. This approach to calculating annual berry yield indices is a promising way for estimating total annual bilberry yields over a given period of time. Models 1 and 2 can be used in conjunction with the Miina et al.’s (2009) bilberry yield model when bilberry coverage, average annual yield and annual variation in the yield are to be predicted in forest planning.

  • Turtiainen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: marjut.turtiainen@uef.fi (email)
  • Miina, Natural Resources Institute Finland (Luke), Management and Production of Renewable Resources, Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: jari.miina@luke.fi
  • Salo, Natural Resources Institute Finland (Luke), Bio-based Business and Industry, Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: kauko.salo@luke.fi
  • Hotanen, Natural Resources Institute Finland (Luke), Management and Production of Renewable Resources, Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: juha-pekka.hotanen@luke.fi

Category: Article

article id 5616, category Article
Hannu Hökkä, Virpi Alenius, Timo Penttilä. (1997). Individual-tree basal area growth models for Scots pine, pubescent birch and Norway spruce on drained peatlands in Finland. Silva Fennica vol. 31 no. 2 article id 5616. https://doi.org/10.14214/sf.a8517

Models for individual-tree basal area growth were constructed for Scots pine (Pinus sylvestris L.), pubescent birch (Betula pubescens Ehrh.) and Norway spruce (Picea abies (L.) Karst.) growing in drained peatland stands. The data consisted of two separate sets of permanent sample plots forming a large sample of drained peatland stands in Finland. The dependent variable in all models was the 5-year basal area growth of a tree. The independent tree-level variables were tree dbh, tree basal area, and the sum of the basal area of trees larger than the target tree. Independent stand-level variables were stand basal area, the diameter of the tree of median basal area, and temperature sum. Categorical variables describing the site quality, as well as the condition and age of drainage, were used. Differences in tree growth were used as criteria in reclassifying the a priori site types into new yield classes by tree species. All models were constructed as mixed linear models with a random stand effect. The models were tested against the modelling data and against independent data sets.

  • Hökkä, ORCID ID:E-mail:
  • Alenius, ORCID ID:E-mail:
  • Penttilä, ORCID ID:E-mail:
article id 5553, category Article
Annika Kangas, Kari T. Korhonen. (1995). Generalizing sample tree information with semiparametric and parametric models. Silva Fennica vol. 29 no. 2 article id 5553. https://doi.org/10.14214/sf.a9204

Semiparametric models, ordinary regression models and mixed models were compared for modelling stem volume in National Forest Inventory data. MSE was lowest for the mixed model. Examination of spatial distribution of residuals showed that spatial correlation of residuals is lower for semiparametric and mixed models than for parametric models with fixed regressors. Mixed models and semiparametric models can both be used for describing the effect of geographic location on stem form.

  • Kangas, ORCID ID:E-mail:
  • Korhonen, ORCID ID:E-mail:
article id 5546, category Article
Oliver Schabenberger, Timothy G. Gregoire. (1995). A conspectus on Estimating Function theory and its applicability to recurrent modeling issues in forest biometry. Silva Fennica vol. 29 no. 1 article id 5546. https://doi.org/10.14214/sf.a9197

Much of forestry data is characterized by a longitudinal or repeated measures structure where multiple observations taken on some units of interest are correlated. Such dependencies are often ignored in favour of an apparently simpler analysis at the cost of invalid inferences. The last decade has brought to light many new statistical techniques that enable one to successfully deal with dependent observations. Although apparently distinct at first, the theory of Estimating Functions provides a natural extension of classical estimation that encompasses many of these new approaches. This contribution introduces Estimating Function Theory as a principle with potential for unification and presents examples covering a variety of modelling issues to demonstrate its applicability.

  • Schabenberger, ORCID ID:E-mail:
  • Gregoire, ORCID ID:E-mail:

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