Scale Analysis

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Marcel A. Croon - One of the best experts on this subject based on the ideXlab platform.

  • Standard Errors and Confidence Intervals for Scalability Coefficients in Mokken Scale Analysis Using Marginal Models
    Sociological Methodology, 2013
    Co-Authors: Renske E. Kuijpers, L. Andries Van Der Ark, Marcel A. Croon
    Abstract:

    Mokken Scale Analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a Scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire Scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for Scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken Scale Analysis. Second, we proved that the method can be applied to Scales consisting of large numbers of items. Third, we applied Mokken Scale Analysis to a set of polytomous items measuring tolerance. The Analysis showed that ignoring standard errors of scalability coefficients might result in incorrect inferences. Keywords: Mokken Scale Analysis, standard errors, scalability coefficients, marginal models

  • Standard Errors and Confidence Intervals for Scalability Coefficients in Mokken Scale Analysis Using Marginal Models
    Sociological Methodology, 2013
    Co-Authors: Renske E. Kuijpers, Marcel A. Croon
    Abstract:

    Mokken Scale Analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a Scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire Scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for Scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken Scale Analysis. Second, w...

  • Mokken Scale Analysis for Dichotomous Items Using Marginal Models
    Psychometrika, 2007
    Co-Authors: L. Andries Van Der Ark, Marcel A. Croon, Klaas Sijtsma
    Abstract:

    Scalability coefficients play an important role in Mokken Scale Analysis. For a set of items, scalability coefficients have been defined for each pair of items, for each individual item, and for the entire Scale. Hypothesis testing with respect to these scalability coefficients has not been fully developed. This study introduces marginal modelling as a framework to derive the standard errors for the scaling coefficients and test hypotheses about these coefficients. Several examples demonstrate the possibilities of marginal modelling in Mokken Scale Analysis. These possibilities include testing whether Mokken’s criteria for a Scale are satisfied, testing whether scalability coefficients of different items are equal, and testing whether scalability coefficients are equal across different groups.

  • Mokken Scale Analysis for Dichotomous Items Using Marginal Models
    Psychometrika, 2007
    Co-Authors: Marcel A. Croon, Klaas Sijtsma
    Abstract:

    Scalability coefficients play an important role in Mokken Scale Analysis. For a set of items, scalability coefficients have been defined for each pair of items, for each individual item, and for the entire Scale. Hypothesis testing with respect to these scalability coefficients has not been fully developed. This study introduces marginal modelling as a framework to derive the standard errors for the scaling coefficients and test hypotheses about these coefficients. Several examples demonstrate the possibilities of marginal modelling in Mokken Scale Analysis. These possibilities include testing whether Mokken’s criteria for a Scale are satisfied, testing whether scalability coefficients of different items are equal, and testing whether scalability coefficients are equal across different groups.

Mubarak Shah - One of the best experts on this subject based on the ideXlab platform.

  • video scene understanding using multi Scale Analysis
    International Conference on Computer Vision, 2009
    Co-Authors: Yang Yang, Jingen Liu, Mubarak Shah
    Abstract:

    We propose a novel method for automatically discovering key motion patterns happening in a scene by observing the scene for an extended period. Our method does not rely on object detection and tracking, and uses low level features, the direction of pixel wise optical flow. We first divide the video into clips and estimate a sequence of flow-fields. Each moving pixel is quantized based on its location and motion direction. This is essentially a bag of words representation of clips. Once a bag of words representation is obtained, we proceed to the screening stage, using a measure called the ‘conditional entropy’. After obtaining useful words we apply Diffusion maps. Diffusion maps framework embeds the manifold points into a lower dimensional space while preserving the intrinsic local geometric structure. Finally, these useful words in lower dimensional space are clustered to discover key motion patterns. Diffusion map embedding involves diffusion time parameter which gives us ability to detect key motion patterns at different Scales using multi-Scale Analysis. In addition, clips which are represented in terms of frequency of motion patterns can also be clustered to determine multiple dominant motion patterns which occur simultaneously, providing us further understanding of the scene. We have tested our approach on two challenging datasets and obtained interesting and promising results.

  • ICCV - Video Scene Understanding Using Multi-Scale Analysis
    2009 IEEE 12th International Conference on Computer Vision, 2009
    Co-Authors: Yang Yang, Jingen Liu, Mubarak Shah
    Abstract:

    We propose a novel method for automatically discovering key motion patterns happening in a scene by observing the scene for an extended period. Our method does not rely on object detection and tracking, and uses low level features, the direction of pixel wise optical flow. We first divide the video into clips and estimate a sequence of flow-fields. Each moving pixel is quantized based on its location and motion direction. This is essentially a bag of words representation of clips. Once a bag of words representation is obtained, we proceed to the screening stage, using a measure called the ‘conditional entropy’. After obtaining useful words we apply Diffusion maps. Diffusion maps framework embeds the manifold points into a lower dimensional space while preserving the intrinsic local geometric structure. Finally, these useful words in lower dimensional space are clustered to discover key motion patterns. Diffusion map embedding involves diffusion time parameter which gives us ability to detect key motion patterns at different Scales using multi-Scale Analysis. In addition, clips which are represented in terms of frequency of motion patterns can also be clustered to determine multiple dominant motion patterns which occur simultaneously, providing us further understanding of the scene. We have tested our approach on two challenging datasets and obtained interesting and promising results.

Renske E. Kuijpers - One of the best experts on this subject based on the ideXlab platform.

  • Standard Errors and Confidence Intervals for Scalability Coefficients in Mokken Scale Analysis Using Marginal Models
    Sociological Methodology, 2013
    Co-Authors: Renske E. Kuijpers, L. Andries Van Der Ark, Marcel A. Croon
    Abstract:

    Mokken Scale Analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a Scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire Scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for Scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken Scale Analysis. Second, we proved that the method can be applied to Scales consisting of large numbers of items. Third, we applied Mokken Scale Analysis to a set of polytomous items measuring tolerance. The Analysis showed that ignoring standard errors of scalability coefficients might result in incorrect inferences. Keywords: Mokken Scale Analysis, standard errors, scalability coefficients, marginal models

  • Standard Errors and Confidence Intervals for Scalability Coefficients in Mokken Scale Analysis Using Marginal Models
    Sociological Methodology, 2013
    Co-Authors: Renske E. Kuijpers, Marcel A. Croon
    Abstract:

    Mokken Scale Analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a Scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire Scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for Scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken Scale Analysis. Second, w...

Yang Yang - One of the best experts on this subject based on the ideXlab platform.

  • video scene understanding using multi Scale Analysis
    International Conference on Computer Vision, 2009
    Co-Authors: Yang Yang, Jingen Liu, Mubarak Shah
    Abstract:

    We propose a novel method for automatically discovering key motion patterns happening in a scene by observing the scene for an extended period. Our method does not rely on object detection and tracking, and uses low level features, the direction of pixel wise optical flow. We first divide the video into clips and estimate a sequence of flow-fields. Each moving pixel is quantized based on its location and motion direction. This is essentially a bag of words representation of clips. Once a bag of words representation is obtained, we proceed to the screening stage, using a measure called the ‘conditional entropy’. After obtaining useful words we apply Diffusion maps. Diffusion maps framework embeds the manifold points into a lower dimensional space while preserving the intrinsic local geometric structure. Finally, these useful words in lower dimensional space are clustered to discover key motion patterns. Diffusion map embedding involves diffusion time parameter which gives us ability to detect key motion patterns at different Scales using multi-Scale Analysis. In addition, clips which are represented in terms of frequency of motion patterns can also be clustered to determine multiple dominant motion patterns which occur simultaneously, providing us further understanding of the scene. We have tested our approach on two challenging datasets and obtained interesting and promising results.

  • ICCV - Video Scene Understanding Using Multi-Scale Analysis
    2009 IEEE 12th International Conference on Computer Vision, 2009
    Co-Authors: Yang Yang, Jingen Liu, Mubarak Shah
    Abstract:

    We propose a novel method for automatically discovering key motion patterns happening in a scene by observing the scene for an extended period. Our method does not rely on object detection and tracking, and uses low level features, the direction of pixel wise optical flow. We first divide the video into clips and estimate a sequence of flow-fields. Each moving pixel is quantized based on its location and motion direction. This is essentially a bag of words representation of clips. Once a bag of words representation is obtained, we proceed to the screening stage, using a measure called the ‘conditional entropy’. After obtaining useful words we apply Diffusion maps. Diffusion maps framework embeds the manifold points into a lower dimensional space while preserving the intrinsic local geometric structure. Finally, these useful words in lower dimensional space are clustered to discover key motion patterns. Diffusion map embedding involves diffusion time parameter which gives us ability to detect key motion patterns at different Scales using multi-Scale Analysis. In addition, clips which are represented in terms of frequency of motion patterns can also be clustered to determine multiple dominant motion patterns which occur simultaneously, providing us further understanding of the scene. We have tested our approach on two challenging datasets and obtained interesting and promising results.

L. Andries Van Der Ark - One of the best experts on this subject based on the ideXlab platform.

  • Standard Errors and Confidence Intervals for Scalability Coefficients in Mokken Scale Analysis Using Marginal Models
    Sociological Methodology, 2013
    Co-Authors: Renske E. Kuijpers, L. Andries Van Der Ark, Marcel A. Croon
    Abstract:

    Mokken Scale Analysis is a popular method for scaling dichotomous and polytomous items. Whether or not items form a Scale is determined by three types of scalability coefficients: (1) for pairs of items, (2) for items, and (3) for the entire Scale. It has become standard practice to interpret the sample values of these scalability coefficients using Mokken’s guidelines, which have been available since the 1970s. For valid assessment of the scalability coefficients, the standard errors of the scalability coefficients must be taken into account. So far, standard errors were not available for Scales consisting of Likert items, the most popular item type in sociology, and standard errors could only be computed for dichotomous items if the number of items was small. This study solves these two problems. First, we derived standard errors for Mokken’s scalability coefficients using a marginal modeling framework. These standard errors can be computed for all types of items used in Mokken Scale Analysis. Second, we proved that the method can be applied to Scales consisting of large numbers of items. Third, we applied Mokken Scale Analysis to a set of polytomous items measuring tolerance. The Analysis showed that ignoring standard errors of scalability coefficients might result in incorrect inferences. Keywords: Mokken Scale Analysis, standard errors, scalability coefficients, marginal models

  • Robust Mokken Scale Analysis by Means of the Forward Search Algorithm for Outlier Detection
    Multivariate behavioral research, 2011
    Co-Authors: Wobbe P. Zijlstra, L. Andries Van Der Ark, Klaas Sijtsma
    Abstract:

    Exploratory Mokken Scale Analysis (MSA) is a popular method for identifying Scales from larger sets of items. As with any statistical method, in MSA the presence of outliers in the data may result in biased results and wrong conclusions. The forward search algorithm is a robust diagnostic method for outlier detection, which we adapt here to identify outliers in MSA. This adaptation involves choices with respect to the algorithm's objective function, selection of items from samples without outliers, and scalability criteria to be used in the forward search algorithm. The application of the adapted forward search algorithm for MSA is demonstrated using real data. Recommendations are given for its use in practical Scale Analysis.

  • Mokken Scale Analysis for Dichotomous Items Using Marginal Models
    Psychometrika, 2007
    Co-Authors: L. Andries Van Der Ark, Marcel A. Croon, Klaas Sijtsma
    Abstract:

    Scalability coefficients play an important role in Mokken Scale Analysis. For a set of items, scalability coefficients have been defined for each pair of items, for each individual item, and for the entire Scale. Hypothesis testing with respect to these scalability coefficients has not been fully developed. This study introduces marginal modelling as a framework to derive the standard errors for the scaling coefficients and test hypotheses about these coefficients. Several examples demonstrate the possibilities of marginal modelling in Mokken Scale Analysis. These possibilities include testing whether Mokken’s criteria for a Scale are satisfied, testing whether scalability coefficients of different items are equal, and testing whether scalability coefficients are equal across different groups.

  • Mokken Scale Analysis in R
    Journal of Statistical Software, 2007
    Co-Authors: L. Andries Van Der Ark
    Abstract:

    Mokken Scale Analysis (MSA) is a scaling procedure for both dichotomous and polytomous items. It consists of an item selection algorithm to partition a set of items into Mokken Scales and several methods to check the assumptions of two nonparametric item response theory models: the monotone homogeneity model and the double monotonicity model. First, we present an R package mokken for MSA and explain the procedures. Second, we show how to perform MSA in R using test data obtained with the Adjective Checklist.

  • Mokken Scale Analysis Using Hierarchical Clustering Procedures
    Applied Psychological Measurement, 2004
    Co-Authors: Alexandra A. H. Van Abswoude, Jeroen K. Vermunt, Bas T. Hemker, L. Andries Van Der Ark
    Abstract:

    Mokken Scale Analysis (MSA) can be used to assess and build unidimensional Scales from an item pool that is sensitive to multiple dimensions. These Scales satisfy a set of scaling conditions, one o...