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• 1.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science, Statistics.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science, Statistics.
Exploratory analysis of intradaily stock returns: a semi Markov chain approach2004Report (Other academic)

In this paper, we study the intradaily distributional and temporal properties of the IBM stock in the time period November 1990 until February 1991. We do this by exploratory analysis by means of semi Markov chains, i. e. a Markov chain where time between events is considered random. Furthermore, the behaviour of the methods is studied under some commonly used models.

• 2.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
A long memory panel unit root test: PPP revisited1999Report (Other academic)
• 3.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science, Statistics.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science, Statistics.
Modeling the distribution of financial returns by functional data analysis2002Report (Other academic)

In this paper, we use functional data analysis to model a time varying unconditional distribution of financial intraday returns. This is in the spirit of the recent development of realized volatility modeling (e.g. Andersen et al, 2001), where one of the moments of this unconditional distribution, the realized volatility, is assumed to change smoothly over time. In the approach used in this paper we instead assume that the entire distribution function changes smoothly over time. This enables us to study auto- and cross dependencies of different parts of the unconditional distribution with no model assumptions but the smoothness of the distribution function. We develop a simulation based procedure for statistical inference of the model. Finally, we apply the method to the Swiss Franc-US Dollar exchange rate 1985-1991.

• 4.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Volatility modeling in the presence of measurement errors2001In: Journal of Risk, ISSN 1465-1211, Vol. 3, no 4, p. 53-67Article in journal (Refereed)

In this paper, the authors examine the effects of measurement errors on volatility measures. This is done by first expressing the moment properties of general volatility models with measurement errors in terms of the corresponding moments for the underlying unobserved signal process. Then the consequences of measurement errors for some GARCH and stochastic volatility models are evaluated. It is shown that measurement error causes the autocorrelation function, here for the squared process, to start and remain lower than for the underlying unobserved signal process. The size of the effects are highly dependent on the degree of persistence in the volatility. Finally, the consequences of measurement errors on time-varying VaR measures are studied.

• 5.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Economics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Testing for unit root against stationarity using the likelihood ratio test2007In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 36, no 2, p. 391-412Article in journal (Refereed)

In a first order autoregressive model with drift, we derive the likelihood ratio test for a unit root against the stationary alternative. We also derive the test in a state space model with trend. Finite sample and asymptotic critical values are obtained by Monte Carlo simulations. A simulation study investigates the power performance of the likelihood ratio test and we also examine how a bias correction of the test affects the results.

• 6.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Klassificeringsförmåga vid komplett cytogenetisk respons för patienter med kronisk myeloisk leukemi: En komparativ studie mellan metoderna diskriminantanalys och logistisk regression2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Kronisk Myeloisk Leukemi (KML) är en form av blodcancer som idag har goda behandlingsmöjligheter och en hög andel överlevande. Vid behandling av sjukdomen mäts responsen efter 12 månader genom att undersöka om patienten uppnått MMR, komplett cytogenetisk respons. Målet i denna uppsats är att hitta variabler som skiljer de patienter som visar eftersökt respons från dem som inte gör det – för att kunna konstruera en modell som skiljer dessa båda grupper åt och som har en god förmåga att klassificera observationerna.

Modellen konstrueras med hjälp av metoden diskriminantanalys och baseras på ett datamaterial som är en sammanställning av tre olika studier. Klassificeringsresultatet för den aktuella metoden jämförs med en logistisk regressions resultat av samma datamaterial med avseende på metodernas förmåga till klassificering av individer. Variablerna som inkluderas i den slutgiltiga diskriminantanalysen är typ av behandling, riskgrupp, hemoglobinhalt, andel vita blodkroppar, kön och respons på behandling efter 3 månader. Klassificeringsförmågan är marginellt bättre än för den logistiska regressionen.

• 7.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Economics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Does Microfinance Empower Women?: Evidence from Self Help Groups in India2007Report (Other academic)

Microfinance programs like the Self Help Bank Linkage Program in India have been increasingly promoted for their positive economic impact and the belief that they empower women. However, only a few studies rigorously examine the link between microfinance and women’s empowerment. This paper contributes by arguing that women empowerment takes place when women challenge the existing social norms and culture, to effectively improve their well being. It empirically validates this hypothesis by using quasi-experimental household sample data collected for five states in India for 2000 and 2003. A general structural model is estimated by employing appropriate techniques to treat the ordinal variables in  order to estimate the impact of the Self Help Group (SHG) on women empowerment for 2000 and 2003. The results strongly demonstrate that on average, there is a significant increase in the women empowerment of the SHG members group. No such significant change is observed however, for the members of the control group. The elegance of the result lies in the fact that the group of SHG participants show clear evidence of a significant and higher empowerment, while allowing for the possibility that some members might have been more empowered than others.

• 8.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Economics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Economic or Non-Economic Factors – What Empowers Women?2008Report (Other academic)

Microfinance programs like Self Help Group Bank linkage program (SHG), aim to empower women through provision of financial services. We investigate this further to determine whether it is the economic or the non-economic factors that have a greater impact on empowering women. Using household survey data on SHG from India, a general structural model is adopted where the latent women empowerment and its latent components (economic factors and financial confidence, managerial control, behavioural changes, education and networking, communication and political participation and awareness) are measured using observed indicators. The results show that for SHG members, economic factors, managerial control and behavioural changes are the most significant factors in empowering women.

• 9.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Economics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Does microfinance empower women?: Evidence from self-help groups in India2009In: International review of applied economics, ISSN 0269-2171, E-ISSN 1465-3486, Vol. 23, no 5, p. 541-556Article in journal (Refereed)

Microfinance programmes like the Self Help Bank Linkage Program in India have been increasingly promoted for their positive economic impact and the belief that they empower women. However, only a few studies rigorously examine the link between microfinance and women's empowerment. This article contributes to this discussion by arguing that women's empowerment takes place when women challenge the existing social norms and culture, to effectively improve their well-being. It empirically validates this hypothesis by using quasi-experimental household sample data collected for five states in India for 2000 and 2003. A general model is estimated by employing appropriate techniques to treat the ordinal variables in order to estimate the impact of the Self Help Group (SHG) on women's empowerment for 2000 and 2003. The results strongly demonstrate that on average, there is a significant increase in the empowerment of women in the SHG members group. No such significant change is observed however, for the members of the control group. The elegance of the result lies in the fact that the group of SHG participants show clear evidence of a significant and higher empowerment, while allowing for the possibility that some members might have been more empowered than others.

• 10. Bertilson, Bo C.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Inter-examiner reliability in the assessment of low back pain (LBP) using the Kirkaldy-Willis classification (KWC)2006In: European spine journal, ISSN 0940-6719, E-ISSN 1432-0932, Vol. 15, no 11, p. 1695-1703Article in journal (Refereed)

Reliable classification systems and clinical tests are sought for the care of patients with low back pain (LBP). The objectives of this clinical study were to evaluate inter-examiner reliability in the classification of patients with LBP, the influence of radiological findings on the classification and the reliability of some clinical tests. Two examiners independently assessed 50 outpatients with LBP. Inter-examiner reliability in classification of patients with LBP using Kirkkaldy-Willis classification (KWC) system and in 30 clinical tests was calculated as percentage agreement and kappa coefficients (kappa). Inter-examiner reliability was excellent (kappa > 0.8) for classification according to KWC. Radiological findings did not influence the reliability. Age of the patient, movement range, and pain and neurological signs seemed to guide the decision on classification. The reliability of clinical tests was good (kappa > 0.6) in 6 tests and moderate (kappa > 0.4) in 12 tests. Good inter-examiner reliability was found for the SLR test, movement range and sensibility testing with spurs in dermatome areas. We conclude that the KWC for classifying patients with LBP seems to be a reliable classification system depending on a few key observations and that moderate and good inter-examiner reliability can be achieved in several clinical tests in the assessment of LBP.

• 11.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
En jämförelse mellan ett parametriskt- och ett icke- parametriskt test2009Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis

Statistisk inferens grundar sig ofta i ett fördelningsantagande beträffande den underliggande datagenereringsprocessen. Huruvida antagandet håller eller ej är viktigt för testens validitet. I denna uppsats undersöks likelihoodkvottestet (LR) och Hettmansperger & McKean's test (HM), i en regressionskontext. För LR-testet görs ett normalitetsantagande vilket jämförs mot HM-testet, för vilket ett fördelningsantagande inte behöver göras. Uppsatsen syftar till att jämföra testens styrka för att avgöra vilket av de två som är optimalt. Jämförelsen baseras dels på empiriska data och dels på simulerade data. Det empiriska datasetet återsamplas med icke-parametrisk bootstrap och de simulerade datasetet genereras med parametrisk bootstrap under ett normalfördelningsantagande samt för ett t-fördelningsantagande. Resultaten för det empiriska datasetet tyder på att HM-testet generellt uppnår högst styrka. Utfallet för det simulerade datasetet indikerar att LR- testet generellt erhåller högst styrka. Vid en jämförelse av testernas empiriska signifikansnivåer pekar resultaten på att Likelihoodkvottestet följer den asymptotiska fördelningen tämligen väl medan Hettmansperger & McKean's test konsekvent inflaterar de empiriska signifikansnivåerna.

• 12.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Asymmetrisk volatilitet2008Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Tidigare forskning på finansiella data har visat att det i vissa fall föreligger en negativ korrelation mellan historisk avkastning och framtida volatilitet. Alltså att en negativ nyhet gör att volatiliteten ökar mer än vad en positiv nyhet hade orsakat. Detta fenomen benämns som asymmetrisk volatilitet eller leverage effect och har tydliga ekonomiska och ekonometriska implikationer. Ickelinjära GARCH-modeller och tester har tagits fram för att behandla och undersöka detta fenomen. Då vi skattar modellerna paå den realiserade avkastningen för HQ aktien får vi fram att omvänt resonemang gäller för våra data. Det innebär, för HQ aktien, att en positiv nyhet gör att volatiliteten ökar mer än vad en negativ nyhet av samma storlek hade orsakat.

• 13.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Neuroscience, Pharmacology.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Neuroscience, Pharmacology.
Perspective on Roseroot (Rhodiola rosea) Studies2009In: Planta Medica, ISSN 0032-0943, E-ISSN 1439-0221, Vol. 75, no 11, p. 1187-1190Article in journal (Refereed)

Rhodiola rosea (roseroot) extract is a commercially successful product, primarily used to reduce the effect of fatigue on physical and mental performance. In this perspective we present our investigation of the most recent studies performed on human subjects. With a focus on the statistical methods we found considerable shortcomings in all but one of the studies that claim significant improvement from roseroot extract. Overall, the study designs have not been well explained. Experimental results have been confused and appear to be in some cases incorrect. Some of the conclusions are based on selected results and contradicting data have not been adequately taken into account. We point to other studies of higher quality performed on roseroot, several that found no significant effect and one that did. We conclude that the currently available evidence for the claimed effects is insufficient and that the effect of Rhodiola rosea is in need of further investigation before therapeutic claims can be made.

• 14.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Genetics and Pathology.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Genetics and Pathology.
Biopsy protocol stability in a three-dimensional model of prostate cancer: Changes in cancer yield after adjustment of biopsy positions1999In: Urology, ISSN 0090-4295, E-ISSN 1527-9995, Vol. 54, p. 862-868Article in journal (Refereed)
• 15.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Genetics and Pathology.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Oncology, Radiology and Clinical Immunology, Radiology. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Genetics and Pathology.
Three-dimensional computer reconstruction of prostate cancer from radical prostatectomy specimens: Evaluation of the model by core biopsy simulation1999In: Urology, ISSN 0090-4295, E-ISSN 1527-9995, Vol. 53, p. 192-198Article in journal (Refereed)
• 16.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Psychology.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Psychology. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Ethnic prejudice: A combined personality and social psychology model2009In: Individual Differences Research, ISSN 1541-745X, Vol. 7, no 4, p. 255-264Article in journal (Refereed)
• 17.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
A generalized definition of the polychoric correlation coefficientManuscript (Other academic)

We generalize the polychoric correlation coefficient to a large class of parametric families of bivariate distributions. The generalized definition agrees with the conventional definition on the family of bivariate normal distributions, and with the generalized tetrachoric correlation coefficient for dichotomous variables. Furthermore, we provide some suggestions for goodness-of-fit tests. The theory is illustrated with examples, which show that the distributional assumption can have a substantial impact on the conclusions of the association analysis.

• 18.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
A generalized definition of the tetrachoric correlation coefficientManuscript (Other academic)

We generalize the tetrachoric correlation coefficient to a large class of parametric families of bivariate distributions. We also show that the generalized definition agrees with the conventional definition on the family of bivariate normal distributions. Furthermore, we provide a necessary and sufficient condition for the generalized tetrachoric correlation coefficient to be well defined for a given family of distributions, and some sufficient criteria which can be useful for practical purposes. Moreover, we illustrate with examples how the distributional assumption can have a profound impact on the conclusions of the association analysis. Using S&P 100 stock data, we exemplify the fact that a correct distributional assumption is vitally important for the analysis. Consequently, it is concluded that the tetrachoric correlation coefficient is not robust to changes of the distributional assumption.

• 19.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
An empirical polychoric correlation coefficientManuscript (Other academic)

We propose a new measure of association for ordinal variables. The new measure of association, named the empirical polychoric correlation coefficient, builds upon the polychoric correlation coefficient, but relaxes its fundamental assumption so that an underlying distribution is only assumed to exist, not to be of a particular parametric family. The empirical polychoric correlation coefficient has properties that are superior to those of the polychoric correlation coefficient; it rests on weaker assumptions, it is well defined for every contingency table, and it converges almost surely to the correct theoretical polychoric correlation. Consequentially, the empirical polychoric correlation coefficient is theoretically robust to changes of the distributional assumption, unlike the polychoric correlation coefficient. A simulation study confirms that the empirical coefficient is considerably more robust than the polychoric correlation coefficient, and it also indicates that it has lower standard deviation.

• 20.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Contributions to the Theory of Measures of Association for Ordinal Variables2009Doctoral thesis, comprehensive summary (Other academic)

In this thesis, we consider measures of association for ordinal variables from a theoretical perspective. In particular, we study the phi-coefficient, the tetrachoric correlation coefficient and the polychoric correlation coefficient. We also introduce a new measure of association for ordinal variables, the empirical polychoric correlation coefficient, which has better theoretical properties than the polychoric correlation coefficient, including greatly enhanced robustness.

In the first article, entitled ``On the relation between the phi-coefficient and the tetrachoric correlation coefficient'', we show that under given marginal probabilities there exists a continuous bijection between the two measures of association. Furthermore, we show that the bijection has a fixed point at zero for all marginal probabilities. Consequently, the choice of which of these measures of association to use is for all practical purposes a matter of preference only.

In the second article, entitled ``A generalized definition of the tetrachoric correlation coefficient'', we generalize the tetrachoric correlation coefficient so that a large class of parametric families of bivariate distributions can be assumed as underlying distributions. We also provide a necessary and sufficient condition for the generalized tetrachoric correlation coefficient to be well defined for a given parametric family of bivariate distributions. With examples, we illustrate the effects on the polychoric correlation coefficient of different distributional assumptions.

In the third article, entitled ``A generalized definition of the polychoric correlation coefficient'', we generalize the polychoric correlation coefficient to a large class of parametric families of bivariate distributions, and show that the generalized and the conventional polychoric correlation coefficients agree on the family of bivariate normal distributions. With examples, we illustrate the effects of different distributional assumptions on the polychoric correlation coefficient. In combination with goodness-of-fit p-values, the association analysis can be enriched with a consideration of possible tail dependence.

In the fourth article, we propose a new measure of association for ordinal variables, named the empirical polychoric correlation coefficient. The empirical polychoric correlation coefficient relaxes the fundamental assumption of the polychoric correlation coefficient so that an underlying joint distribution is only assumed to exist, not to be of a particular parametric family. We also provide an asymptotical result, by which the empirical polychoric correlation coefficient converges almost surely to the true polychoric correlation under very general conditions. Thus, the proposed empirical polychoric correlation coefficient has better theoretical properties than the polychoric correlation coefficient.

1. On the relation between the phi-coefficient and the tetrachoric correlation coefficient
Open this publication in new window or tab >>On the relation between the phi-coefficient and the tetrachoric correlation coefficient
##### Abstract [en]

We show existence of a continuous bijection between the tetrachoric correlation coefficient and the phi-coefficient under given marginal probabilities. Implications are that the tetrachoric correlation coefficient can be calculated using the assumptions of the phi-coefficient construction, and the phi-coefficient can be calculated using the assumptions of the tetrachoric correlation construction. As a consequence, whether to use the phi-coefficient or the tetrachoric correlation coefficient is a matter of preference only. The result can also be used to construct a numerical table of tetrachoric correlation coefficients, converted from the marginal probabilities and the phi-coefficient, which is easy to calculate by hand. Moreover, a mathematically rigorous definition of the tetrachoric correlation coefficient is provided, along with a proof that the coefficient is well defined.

##### Keywords
phi-coefficient, tetrachoric correlation coefficient, 2 x 2 contingency table, measure of association, dichotomous variables
##### National Category
Probability Theory and Statistics
Statistics
##### Identifiers
urn:nbn:se:uu:diva-100692 (URN)
Available from: 2009-04-06 Created: 2009-04-06 Last updated: 2011-03-29Bibliographically approved
2. A generalized definition of the tetrachoric correlation coefficient
Open this publication in new window or tab >>A generalized definition of the tetrachoric correlation coefficient
##### Abstract [en]

We generalize the tetrachoric correlation coefficient to a large class of parametric families of bivariate distributions. We also show that the generalized definition agrees with the conventional definition on the family of bivariate normal distributions. Furthermore, we provide a necessary and sufficient condition for the generalized tetrachoric correlation coefficient to be well defined for a given family of distributions, and some sufficient criteria which can be useful for practical purposes. Moreover, we illustrate with examples how the distributional assumption can have a profound impact on the conclusions of the association analysis. Using S&P 100 stock data, we exemplify the fact that a correct distributional assumption is vitally important for the analysis. Consequently, it is concluded that the tetrachoric correlation coefficient is not robust to changes of the distributional assumption.

##### Keywords
tetrachoric correlation, generalization, 2 x 2 contingency table, dichotomous variables, measure of association, robustness
##### National Category
Probability Theory and Statistics
Statistics
##### Identifiers
urn:nbn:se:uu:diva-100694 (URN)
Available from: 2009-04-06 Created: 2009-04-06 Last updated: 2011-03-29Bibliographically approved
3. A generalized definition of the polychoric correlation coefficient
Open this publication in new window or tab >>A generalized definition of the polychoric correlation coefficient
##### Abstract [en]

We generalize the polychoric correlation coefficient to a large class of parametric families of bivariate distributions. The generalized definition agrees with the conventional definition on the family of bivariate normal distributions, and with the generalized tetrachoric correlation coefficient for dichotomous variables. Furthermore, we provide some suggestions for goodness-of-fit tests. The theory is illustrated with examples, which show that the distributional assumption can have a substantial impact on the conclusions of the association analysis.

##### Keywords
polychoric correlation, generalization, contingency table, ordinal variables, measure of association, robustness, goodness-of-fit
##### National Category
Probability Theory and Statistics
Statistics
##### Identifiers
urn:nbn:se:uu:diva-100695 (URN)
Available from: 2009-04-06 Created: 2009-04-06 Last updated: 2011-03-29Bibliographically approved
4. An empirical polychoric correlation coefficient
Open this publication in new window or tab >>An empirical polychoric correlation coefficient
##### Abstract [en]

We propose a new measure of association for ordinal variables. The new measure of association, named the empirical polychoric correlation coefficient, builds upon the polychoric correlation coefficient, but relaxes its fundamental assumption so that an underlying distribution is only assumed to exist, not to be of a particular parametric family. The empirical polychoric correlation coefficient has properties that are superior to those of the polychoric correlation coefficient; it rests on weaker assumptions, it is well defined for every contingency table, and it converges almost surely to the correct theoretical polychoric correlation. Consequentially, the empirical polychoric correlation coefficient is theoretically robust to changes of the distributional assumption, unlike the polychoric correlation coefficient. A simulation study confirms that the empirical coefficient is considerably more robust than the polychoric correlation coefficient, and it also indicates that it has lower standard deviation.

##### Keywords
empirical polychoric correlation coefficient, polychoric correlation, contingency table, ordinal variables, measure of association, robust statistics
##### National Category
Probability Theory and Statistics
Statistics
##### Identifiers
urn:nbn:se:uu:diva-100696 (URN)
Available from: 2009-04-06 Created: 2009-04-06 Last updated: 2011-03-29Bibliographically approved
• 21.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
On the relation between the phi-coefficient and the tetrachoric correlation coefficientManuscript (Other academic)

We show existence of a continuous bijection between the tetrachoric correlation coefficient and the phi-coefficient under given marginal probabilities. Implications are that the tetrachoric correlation coefficient can be calculated using the assumptions of the phi-coefficient construction, and the phi-coefficient can be calculated using the assumptions of the tetrachoric correlation construction. As a consequence, whether to use the phi-coefficient or the tetrachoric correlation coefficient is a matter of preference only. The result can also be used to construct a numerical table of tetrachoric correlation coefficients, converted from the marginal probabilities and the phi-coefficient, which is easy to calculate by hand. Moreover, a mathematically rigorous definition of the tetrachoric correlation coefficient is provided, along with a proof that the coefficient is well defined.

• 22.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Centre for Tabacco Prevention, Huddinge. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Factors affecting reproducibility of dietary reports using food frequency questionnaires2000In: European Journal of Clinical Nutrition, ISSN 0954-3007, E-ISSN 1476-5640, Vol. 54, no 8, p. 658-664Article in journal (Refereed)
• 23.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Neuroscience, Ophthalmology.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Which endpoint: mean intraocular pressure or proportion of successful patients?2003In: Journal of glaucoma, ISSN 1057-0829, E-ISSN 1536-481X, Vol. 12, no 4, p. 321-332Article in journal (Refereed)

A reduction in intraocular pressure in clinical trials can be determined through the mean intraocular pressure, through the proportion of patients who have the intraocular pressure reduced to a specific target intraocular pressure, or both. Since both these possible endpoints measure the shift of 2 intraocular pressure distributions, we recommend that only one of them be tested. In general, testing the difference between mean-values is much more efficient than testing the difference between proportions. However, proportions of successful patients are valuable in showing the clinical implication of a reduction in mean intraocular pressure, particularly when evaluating a moderate pressure reduction. The effect of a small mean intraocular pressure reduction on the probability to reach the target intraocular pressure is pointed out, particularly the fact that it can be substantial even if the mean reduction is smaller than the measurement error.

• 24. Jacobson, Tor
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Inflation, Exchange Rates and PPP in a Multivariate Panel Cointegration Model2008In: Econometrics Journal, ISSN 1368-4221, E-ISSN 1368-423X, Vol. 11, no 1, p. 58-79Article in journal (Refereed)

New multivariate panel cointegration methods are used to analyze nominal exchange rates and prices in four major economies in Europe: France, Germany, Italy and the United Kingdom for the post-Bretton Woods period. We test for purchasing power parity (PPP) between these four countries and find that the theoretical PPP relationship does not hold. However, the estimated unrestricted relationship is found to be remarkably close to the theoretical one (1, -1.5, 0.9 instead of 1, -1,1). Relevant asymptotic results are stated, proved, and evaluated using Monte Carlo simulations. The asymptotic results are general and may hence be used in similar empirical contexts using the same model structure. Parametric bootstrap inference is used in order to deal with test size distortions.

• 25.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Att testa normalitet och heteroskedasticitet i en linjär regressionsmodell: En empirisk jämförelse mellan normalitets-, heteroskedasticitets- och kombinationstest2000Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis

Denna uppsats behandlar frågan om normalitets-, heteroskedasticitets- och kombinationstests användbarhet i att testa nollhypotesen om samtidig normalitet och likhet i varians. Kombinationstesten utgörs här av summan av ett χ2-fördelat normalitetstest och ett χ2-fördelat heteroskedasticitetstest.

Undersökningen handlar dels om testens styrkenivåer under olika former av avvikelser från nollhypotesen, varvid intresset särskilt är inriktat på hur kombinationstesten klarar sig. Men även frågan om normalitets- och heteroskedasticitetstestens förmåga att hålla sina signifikansnivåer under nollhypoteserna om normalitet respektive lika varians när störningstermerna har olika varians respektive ej är normalfördelade tas upp. Undersökningen genomförs med hjälp av omfattande Monte Carlo-simuleringar.

Resultaten pekar på att kombinationstesten klarar sig väl i förhållande till normalitets- respektive heteroskedasticitetstesten när det gäller styrkenivåer, förutom då störningstermerna är symmetriska, platykurtiska och med lika varians. De visar också att ingen av normalitets- eller heteroskedasticitetstesten lyckas hålla sig acceptabelt nära sina nominella signifikansnivåer.

• 26.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Autokorrelationens inverkan på signifikansnivån för Jarque-Beras normalitetstest för regressionsresidualer: En Monte Carlo-studie1999Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Denna uppsats behandlar frågan om hur positivt autokorrelerade störningstermer påverkar signifikansnivån för Jarque-Beras normalitetstest för regressionsresidualer. Därvid genomförs omfattande Monte Carlo-simuleringar med olika α-, ρ-, β-, X- och n-värden. De faktiskt observerade signifikansnivåerna från dessa simuleringar jämförs sedan med de teoretiska signifikansnivåerna från Jarque-Beras normalitetstest för observationer, för att se vilken påverkan autokorrelationen har. Även inverkan på de asymptotiskt kritiska $\chi_{2}^{2}$-värdena behandlas. Slutsatsen från denna uppsats är att autokorrelationens inverkan varierar kraftigt, och är beroende av såväl storleken på α, n och ρ som utseendet på β- och X-värdena. För låga n- och ρ-värden tenderar de faktiskt observerade signifikansnivåerna att vara ungefär lika stora som de teoretiska signifikansnivåerna från Jarque-Beras normalitetstest för observationer, medan de för högre n- och ρ-värden tenderar att vara större.

• 27.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Quantile regression estimation of nonlinear longitudinal data2004Report (Other academic)

This paper examines a weighted version of the quantile regression estimator defined by Koenker and Bassett (1978), adjusted to the case of nonlinear longitudinal data. Different weights are used and compared by computer simulation using a four-parameter logistic growth function and error terms following an AR(1) model. It is found that the estimator is performing quite well, especially for the median regression case, that the differences between the weights are small, and that increasing the correlation in the AR(1) model leads to better behaviour of the estimator. A comparison is made with the corresponding mean regression estimator, which is found to be less robust. Finally the estimator is applied to a data set with growth patterns of two genotypes of soybean.

• 28.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Estimating Nonlinear structural models: EMM and the Kenny-Judd model2007In: Structural Equation Modeling, ISSN 1070-5511, E-ISSN 1532-8007, Vol. 14, no 3, p. 391-403Article in journal (Refereed)

The estimation of nonlinear structural models is not trivial. One reason for this is that a closed form solution of the likelihood may not be feasible or does not exist. We propose to estimate nonlinear structural models using the efficient method of moments, as generating data according to the models is often very easy. A simulation study of the interaction model of Kenny-Judd shows promising results, for example, the bias of the parameter for the interaction effect is less for the efficient method of moments compared to quasi-maximum likelihood (QML) and characteristic function estimator (CFE) (Blom & Christoffersson 2001) and comparable to latent moderated structural equations (LMS) (Schermelleh-Engel, Klein, & Moosbrugger, 1998).

• 29.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Why not use standard panel unit root test for testing PPP2008In: Economics Bulletin, ISSN 1545-2921, E-ISSN 1545-2921, Vol. 3, no 26, p. 1-11Article in journal (Refereed)
• 30.
Friedrich-Schiller-Universität, Jena, Germany.
Friedrich-Schiller-Universität, Jena, Germany . Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Modelling method effects as individual causal effects2008In: Journal of the Royal Statistical Society: Series A (Statistics in Society), ISSN 0964-1998, E-ISSN 1467-985X, Vol. 171, no 1, p. 41-63Article in journal (Refereed)

Method effects often occur when different methods are used for measuring the same construct. We present a new approach for modelling this kind of phenomenon, consisting of a definition of method effects and a first model, the method effect model, that can be used for data analysis. This model may be applied to multitrait-multimethod data or to longitudinal data where the same construct is measured with at least two methods at all occasions. In this new approach, the definition of the method effects is based on the theory of individual causal effects by Neyman and Rubin. Method effects are accordingly conceptualized as the individual effects of applying measurement method j instead of k. They are modelled as latent difference scores in structural equation models. A reference method needs to be chosen against which all other methods are compared. The model fit is invariant to the choice of the reference method. The model allows the estimation of the average of the individual method effects, their variance, their correlation with the traits (and other latent variables) and the correlation of different method effects among each other. Furthermore, since the definition of the method effects is in line with the theory of causality, the method effects may (under certain conditions) be interpreted as causal effects of the method. The method effect model is compared with traditional multitrait-multimethod models. An example illustrates the application of the model to longitudinal data analysing the effect of negatively (such as 'feel bad') as compared with positively formulated items (such as 'feel good') measuring mood states.

• 31.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmacy.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmacy. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmacy. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmacy. Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics. Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmacy.
Adherence to treatment in Swedish HIV infected patients2006In: Journal of Clinical Pharmacy and Therapeutics, ISSN 0269-4727, E-ISSN 1365-2710, Vol. 31, no 6, p. 605-616Article in journal (Refereed)

Objectives: The objectives were to assess the prevalence of adherence to antiretroviral treatment in Swedish human immunodeficiency virus (HIV)-infected patients and to evaluate factors associated with adherence.

Methods: All HIV-treated patients, who attended one of 30 (of a total of 32) Swedish infectious diseases clinics, during 7 months, were asked to complete an anonymous questionnaire containing the 9-item Morisky Medication Adherence Scale (MMAS) and questions about other factors potentially affecting adherence. The summary score of MMAS ranges from 1 to 13, where 13 indicates perfect adherence; patients scoring 11 or above (corresponding to 95% adherence level) were classified as 'adherent'.

Results and discussion: In total 946 patients participated (response rate 97.5%). The proportion of patients who reported not missing a dose during the day prior to the completion of the questionnaire was 97% and the proportion classified as 'adherent' was 63%. 'Adherent' patients were more likely to have a good relationship with their health care professionals (P < 0.05) and not have problems with drugs or alcohol (P < 0.01). Being older (P < 0.01) and having a shorter time on current treatment (P < 0.01) and on treatment in total (P < 0.05) were factors also associated with good adherence.

Conclusion: Factors modifiable for interventions by health care professionals are patient-provider relationship, drug or alcohol problems and patients with long treatment periods.

• 32.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Test of autocorrelation and heteroscedasticity in a regression model in the presence of measurement errors2000Report (Other academic)
• 33.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Test of heteroscedasticity in a regression model in the presence of measurement errors2002In: Economics Letters, ISSN 0165-1765, E-ISSN 1873-7374, Vol. 76, no 2, p. 205-211Article in journal (Refereed)
• 34.
University of Gothenburg, Department of Economics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
A note on the pooling of individual panic unit root tests2009In: Econometric Theory, ISSN 0266-4666, E-ISSN 1469-4360, Vol. 25, no 6, p. 1851-1868Article in journal (Refereed)

One of the most cited studies in recent years within the field of nonstationary panel data analysis is that of Bai and Ng (2004), in which the authors propose PANIC, a new framework for analyzing the nonstationarity of panels with idiosyncratic and common components. The problem is that the asymptotic validity of PANIC as a platform for constructing pooled panel unit root tests based on averaging is not fully proven. This paper provides the required results, whose usefulness is verified through simulations.

• 35.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Information Science, Statistics.
Department of Education, Gothenburg University.
Non-linear structural equation modeling2009In: Structural Equation Modeling in Educational Research: Concepts and Applications / [ed] Timothy Teo and Myint Swe Khine, Rotterdam: SensePublishers , 2009, p. 317-328Chapter in book (Other academic)

Research in the social sciences often includes hypotheses concerning interactive or nonlinear effects on a given outcome latent variable. When it comes to estimating such effects, however, there is lack of consensus on how to do so properly, particularly when performing structural equation modeling (SEM). A plethora of methods have been proposed and discussed, including those de-scribed in Algina and Moulder (2001), Jaccard and Wan (1995), Joreskog and yang (1996,1997), Yang-Jonsson (1997,1998), Klein and Moosbrugger (2000), Klein and Muthen (2002), Marsh,Wen, and Hau (2004), Ping (1996a, 1996b), Schumacker and Marcoulides (1998), and Wall and Amemiya (2001, 2003). Most approaches to latent variable interactions are based on a product indicator methodology originated by Kenny and Judd (1984) that requires a level of technical and computational sophistication that renders them quite inaccessible to the average practitioner. The focus of this chapter is on the discussion of a technically straightforward approach using latent variable scores to estimating interactive and nonlinear effects within SEM. The next section, we will first describe LVS approach in a theoretical framework and in succeeding section, the approach will demonstrate in a practical manner using an empirical data.

To illustrate how latent variable scores can be used to estimate nonlinear relationship between latent variables we will use Reading comprehension model as an example.

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