Measurement models

In order to evaluate the measurement (outer) model, different criteria for reflective and formative constructs are applicable (Hair et al. 2011a). I will thus assess reliability and validity separately for both types of specification. 

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Reviews of concentration polarization have been reported (14,38,39). Because solute wall concentration may not be experimentally measurable, models relating solute and solvent fluxes to hydrodynamic parameters are needed for system design. The Navier-Stokes diffusion—convection equation has been numerically solved to calculate wall concentration, and thus the water flux and permeate quaUty (40). 

Research use of individual methods or instruments in an academic or basic research environment, with interest centered around obtaining facts and relationships, where specific conditions exist as concerns precision, number of measurements, models, etc. that force the use of particular and/or highly sophisticated statistical techniques. 

M Elimelech, J Gregory, X Jia, RA Williams. Particle Deposition and Aggregation Measuring, Modeling and Simulation. Oxford Butterworth-Heinemann Ltd., 1995. 

Before we introduce the Kalman filter, we reformulate the least-squares algorithm discussed in Chapter 8 in a recursive way. By way of illustration, we consider a simple straight line model which is estimated by recursive regression. Firstly, the measurement model has to be specified, which describes the relationship between the independent variable x, e.g., the concentrations of a series of standard solutions, and the dependent variable, y, the measured response. If we assume a straight line model, any response is described by ... 

After each new observation, the estimates of the model parameters are updated (= new estimate of the parameters). In all equations below we treat the general case of a measurement model with p parameters. For the straight line model p = 2. An estimate of the parameters b based ony - 1 measurements is indicated by b(/ - 1). Let us assume that the parameters are recursively estimated and that an estimate h(j - 1) of the model parameters is available from y - 1 measurements. The next measurement y(j) is then performed at x(j), followed by the updating of the model parameters to b(/). 

The first step of the algorithm is to calculate the innovation (/), which is the difference between measured y(j) and predicted response y(j) at x(j). Therefore, the last estimate b(/ - 1) of the parameters is substituted in the measurement model in order to forecast the response y(j), which is measured at x(j) ... 

The measurement model of the time-invariant calibration system (eq. (41.5)) should now be expanded in the following way ... 

A microturbine with heat recovery was one of the measures modeled. It has not been included in any of the measure sets. A more comprehensive analysis was done that took account of the different treatments of electricity and thermal energy and the effects of varying electricity and natural gas prices. This analysis is available in a separate report [6],... 

We now derive the time-domain solutions of first and second order differential equations. It is not that we want to do the inverse transform, but comparing the time-domain solution with its Laplace transform helps our learning process. What we hope to establish is a better feel between pole positions and dynamic characteristics. We also want to see how different parameters affect the time-domain solution. The results are useful in control analysis and in measuring model parameters. At the end of the chapter, dead time, reduced order model, and the effect of zeros will be discussed. 

Keywords Analytical chemistry, Environmental concentration, Measuring, Modelling, Risk assessment... 

Although theoretical estimates for neutral branching fractions of reactions such as 10 have been attempted, their reliability is suspect.32 In the absence of measurement, modelers have typically assumed equal branching fractions between channels in which one and two hydrogen atoms are separated from the molecular skeleton (e.g. 0.50 for reactions 10a and 10b). New assumptions based on recent experimental work have also been made.33... 

J. Ylen, Measuring, modeling and controlling the pH value and the dynamic chemical state, Dissertation for the degree of Doctor of Science in Technology, Helsinki University of Technology (2001). 

Which of the following equations is the correct one to use to combine standard uncertainties when the measurement model involves only multiplication and/or division ... 

A second use for uncertainty values lies in their potential for helping us to improve our experimental procedures. In calculating the uncertainty for a measurement, we will have assembled a list of standard uncertainties for the variables of the measurement model. If we wish to improve the quality of our measurement, we must look first at the component of the measurement system contributing the largest uncertainty. If this is the dominant contribution to the combined uncertainty, then any attempt to improve other aspects of the measurement process will be a waste of time. By attempting to reduce the size of the dominant uncertainty first, we will produce the greatest return for our effort. 

Elimelech, M., Gregory, J., Jia, X., and Williams, R. A., Particle Deposition and Aggregation, Measurement, Modelling and Simulation . Butterworth-Heinemann, Woburn (1995). 

Ruscio, J., St Ruscio, A. M. (2002). A structure-based approach to psychological measurement Matching measurement models to latent structure. Assessment, 9, 4-16. 

Anaerobic conditions in wastewater of sewer systems may give rise to formation of volatile substances that are typically identified by a number of problems, like malodors, health risks and corrosion. The conditions and processes related to such problems are dealt with in Section 3.2.2. Further information on measurement, modeling and control of odors can be found in Stuetz and Frechen (2001). 

Since the data are usually obtained from observations (measurements) that are subject to probabilistic fluctuations, redundant data are usually inconsistent in the sense that each sufficient subset yields different results from other subsets. To obtain a unique solution, an additional criterion is necessary. If the least square principle is applied, among all the solutions that are consistent with the measurement model, the estimations that are as close as possible to the measurements are considered to be the solution of the estimation problem. We define a least squares estimation problem as follows ... 

If the state of the system is directly measured, then the measurement model is represented by... 

In this section we develop the best linear estimate of x for the general linear measurement model... 

Estimate x given that the previous measurement model holds and, further, that the set of linear constraints is satisfied with an additive random component w ... 

If combinations of leaks and measurement biases are considered, both the measurement model and the process constraints equations need to be modified. The formulation for the least squares problem is now... 

Let us state the measurement model for the ith observation as the sum of the true state being measured and an additive error, that is,... 

Nghiem LD, Schafer AI, Elimelech M (2004) Removal of natural hormones by nanofiltration membranes measurement, modeling, and mechanisms. Environ Sci Technol 38 1888-1896... 

Combined Standard Uncertainty is the standard uncertainty that is obtained by combining (root of the sum of squares) individual standard measurement uncertainties associated with the input quantities in a measurement model. 

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