The Cholesky Factorization of the Inverse Correlation or Covariance Matrix in Multiple Regression

Technometrics ◽  
1982 ◽  
Vol 24 (3) ◽  
pp. 191-198 ◽  
Author(s):  
Douglas M. Hawkins ◽  
W. J. R. Eplett
Keyword(s):  
Multiple Regression ◽  
Covariance Matrix ◽  
Inverse Correlation ◽  
Cholesky Factorization

scholarly journals Electrical resistance properties of tree tissues in cankers incited by Endothiaparasitica and Nectriagalligena

1978 ◽  
Vol 8 (2) ◽  
pp. 162-167 ◽  
Author(s):  
David M. Sylvia ◽  
Terry A. Tattar
Keyword(s):  
Moisture Content ◽  
Multiple Regression ◽  
Electrical Resistance ◽  
Current Flow ◽  
Inverse Correlation ◽  
Vertical Axis ◽  
Healthy Tissue ◽  
Stem Tissue ◽  
Regression Analyses ◽  
Cation Concentration

Electrical resistance (ER) measurements were taken with a Shigometer across tree cankers found on Castaneadentata, Betulalenta, and B. populifolia. Cankers were incited by Endothiaparasitica and Nectriagalligena, respectively. Measurements taken along the vertical axis of the stem were at 2-cm intervals from 8 cm above the canker margin to 8 cm below the canker. Three zones of electrical character were distinguished. The canker margin exhibited decreased ER as compared with healthy tissue, whereas ER increased in the canker face. Moisture content, mobile cation concentration, and the path of current flow were all found to contribute to ER. Multiple regression analyses indicated fundamental changes in the variables contributing to ER in summer and winter samples. Strong inverse relationships were found between ER and total ash and between ER and potassium concentrations in September. February samples, however, exhibited an inverse correlation between ER and moisture content. These data indicated that moisture was the dominating factor in ER measurements of stem tissue in the winter.

Total Convection Affects Serum β2 Microglobulin and C-Reactive Protein but Not Erythropoietin Requirement following Post-Dilutional Hemodiafiltration

2015 ◽  
Vol 41 (6) ◽  
pp. 494-501 ◽  
Author(s):  
Ezio Movilli ◽  
Corrado Camerini ◽  
Paola Gaggia ◽  
Roberto Zubani ◽  
Paolo Feller ◽  
...  
Keyword(s):  
Multiple Regression ◽  
Treatment Time ◽  
Transferrin Saturation ◽  
Inverse Correlation ◽  
Control Group ◽  
Study Group ◽  
C Reactive Protein ◽  
Β2 Microglobulin ◽  
Reactive Protein

Background: Inflammation and increased erythropoiesis stimulating agents (ESA) requirement are frequently associated in patients on dialysis. On-line hemodiafiltration (ol-HDF), putting together high levels of diffusion, and convection could improve both conditions. However, it is still not known which depurative component plays a major role in determining this result. The aim of the study was to evaluate the role of convection and diffusion on long-term variations of serum β2 microglobulin (Δβ2M), high-sensitive C-reactive protein (ΔhsCRP) concentrations, and ESA requirement (ΔESA) in ol-HDF. Methods: Seventy-three patients prevalent on high flux HD (hfHD) were studied. Thirty-eight patients were switched from hfHD to post-dilutional ol-HDF (Study group); the other 35 patients were considered the Control group. At 6 and 12 months, the effects of ol-HDF and hfHD on ΔhsCRP, ΔB2M, and ΔESA (U/kg/week) were evaluated. Other variables considered were body weight (BW), serum albumin (sAlb), hemoglobin (Hb), and equilibrated Kt/V (eKt/V). Iron therapy and ESA were administered intravenously according to the K/DOQI guidelines in order to maintain transferrin saturation between 20 and 40%, serum ferritin between 150 and 500 ng/ml and Hb between 11 and 12 g/dl. Qb, treatment time and Qd remained constant. Ol-HDF and hfHD were performed using membranes of size 1.9-2.1 sqm. Ultrapure dialysate and substitution fluid were employed in both HDF and HD treatments. Data are expressed as mean ± SD. Paired t test, Mann-Whitney U test, and simple and multiple regression analyses were employed for statistical evaluation. Results: Study group: total convective volume (TCV) was 22.1 ± 1.9 l/session. A significant reduction of hsCRP: from 6.8 ± 7.1 to 2.3 ± 2.4 mg/dl (p < 0.001), β2M: from 36.5 ± 14.4 to 24.7 ± 8.6 mg/dl (p < 0.0001) and ESAdose: from 107 ± 67 to 65 ± 44 U/kg/week (p < 0.005) was observed. No significant variations of Hb, BW and sAlb were seen. A significant inverse correlation was found between TCV and Δβ2M (r = -0.627; p < 0.0001), and TCV and ΔhsCRP (r = -0.514; p < 0.0001); no correlation between TCV and ΔESAdose was observed. No correlation was found between eKt/V and Δβ2M, ΔhsCRP, and ΔESAdose. Multiple regression analysis with ΔESAdose as dependent variable showed ΔhsCRP as the only significantly associated independent factor (p < 0.01). Control group: no significant variations of hsCRP, β2M, and ESAdose were observed over time. Conclusions: Ol-HDF induces a long-term significant reduction in pre-dialysis β2M and hsCRP concentrations. The magnitude of reduction is directly correlated to the amount of TCV achieved but not on eKt/V. The observed reduction in ESAdose requirement is independent either on convection or diffusion, but is directly associated to the concomitant reduction of inflammation.

scholarly journals Fast Sparse Gaussian Markov Random Fields Learning Based on Cholesky Factorization

2017 ◽  
Author(s):  
Ivan Stojkovic ◽  
Vladisav Jelisavcic ◽  
Veljko Milutinovic ◽  
Zoran Obradovic
Keyword(s):  
Covariance Matrix ◽  
Health Informatics ◽  
Markov Random Fields ◽  
Cholesky Factorization ◽  
Active Set ◽  
Solution Quality ◽  
Precision Matrix ◽  
Penalty Term ◽  
Markov Random ◽  
Inverse Covariance Matrix

Learning the sparse Gaussian Markov Random Field, or conversely, estimating the sparse inverse covariance matrix is an approach to uncover the underlying dependency structure in data. Most of the current methods solve the problem by optimizing the maximum likelihood objective with a Laplace prior L1 on entries of a precision matrix. We propose a novel objective with a regularization term which penalizes an approximate product of the Cholesky decomposed precision matrix. This new reparametrization of the penalty term allows efficient coordinate descent optimization, which in synergy with an active set approach results in a very fast and efficient method for learning the sparse inverse covariance matrix. We evaluated the speed and solution quality of the newly proposed SCHL method on problems consisting of up to 24,840 variables. Our approach was several times faster than three state-of-the-art approaches. We also demonstrate that SCHL can be used to discover interpretable networks, by applying it to a high impact problem from the health informatics domain.

Language and Literacy Predictors of Dialect Density Among School-Age African American Children From Two Geographic Regions

2020 ◽  
Vol 51 (3) ◽  
pp. 807-820
Author(s):  
Lena G. Caesar ◽  
Marie Kerins
Keyword(s):  
African American ◽  
Multiple Regression ◽  
Oral Language ◽  
East Coast ◽  
Geographic Region ◽  
Literacy Skills ◽  
School Age ◽  
Regression Analyses ◽  
Geographic Regions ◽  
American Children

Purpose The purpose of this study was to investigate the relationship between oral language, literacy skills, age, and dialect density (DD) of African American children residing in two different geographical regions of the United States (East Coast and Midwest). Method Data were obtained from 64 African American school-age children between the ages of 7 and 12 years from two geographic regions. Children were assessed using a combination of standardized tests and narrative samples elicited from wordless picture books. Bivariate correlation and multiple regression analyses were used to determine relationships to and relative contributions of oral language, literacy, age, and geographic region to DD. Results Results of correlation analyses demonstrated a negative relationship between DD measures and children's literacy skills. Age-related findings between geographic regions indicated that the younger sample from the Midwest outscored the East Coast sample in reading comprehension and sentence complexity. Multiple regression analyses identified five variables (i.e., geographic region, age, mean length of utterance in morphemes, reading fluency, and phonological awareness) that accounted for 31% of the variance of children's DD—with geographic region emerging as the strongest predictor. Conclusions As in previous studies, the current study found an inverse relationship between DD and several literacy measures. Importantly, geographic region emerged as a strong predictor of DD. This finding highlights the need for a further study that goes beyond the mere description of relationships to comparing geographic regions and specifically focusing on racial composition, poverty, and school success measures through direct data collection.

Clinical factors correlated with vitamin D deficiency in patients with obesity scheduled for bariatric surgery: A single center experience

2020 ◽  
Vol 90 (3-4) ◽  
pp. 346-352
Author(s):  
Vincenzo Pilone ◽  
Salvatore Tramontano ◽  
Carmen Cutolo ◽  
Federica Marchese ◽  
Antonio Maria Pagano ◽  
...  
Keyword(s):  
Bariatric Surgery ◽  
Vitamin D ◽  
Vitamin D Deficiency ◽  
Serum Vitamin ◽  
Inverse Correlation ◽  
Model Assessment ◽  
Cross Sectional ◽  
Serum Vitamin D ◽  
Female Sex ◽  
Vitamin D Levels

Abstract. We aim to assess the prevalence of vitamin D deficiency (VDD) in patients scheduled for bariatric surgery (BS), and to identify factors that might be associated with VDD. We conducted a cross-sectional observational study involving all consecutive patients scheduled for BS from 2017 to 2019. The exclusion criteria were missing data for vitamin D levels, intake of vitamin D supplements in the 3 months prior to serum vitamin D determination, and renal insufficiency. A total of 206 patients (mean age and body mass index [BMI] of 34.9 ± 10.7 years, and 44.3 ± 6.99 kg/m2, respectively) met the inclusion criteria and were enrolled for data analysis. VDD (<19.9 ng/mL), severe VDD (<10 ng/mL), and vitamin D insufficiency (20–29.9 ng/mL) were present in 68.8 %, 12.5 %, and 31.2 % of patients, respectively. A significant inverse correlation was found between vitamin D levels and initial BMI, parathyroid hormone, and homeostatic model assessment of insulin resistance (r = −0.280, p < 0.05; r = −0.407, p = 0.038; r = −0.445, p = 0.005), respectively. VDD was significantly more prevalent in patients with higher BMI [−0.413 ± 0.12, CI95 % (−0.659; −0.167), p = 0.006], whereas no significant association between hypertension [−1.005 ± 1.65, CI95 % (−4.338; 2.326), p = 0.001], and diabetes type 2 (T2D) [−0.44 ± 2.20, CI95 % (−4.876; 3.986), p = 0.841] was found. We observed significant association between female sex and levels of vitamin D [6.69 ± 2.31, CI95 % (2.06; 11.33), p = 0.006]. The present study shows that in patients scheduled for BS, VDD deficiency is common and was associated with higher BMI, and female sex.

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