Factor Analysis And Confirmatory Factor Analysis Essay Example for Free

Factor Analysis And Confirmatory Factor Analysis Essay Factor analysis is an arithmetical technique used to describe variability regarding observed variables with regard to lower number of unobserved variables. Factor analysis looks for such joint variations in response to unobserved hidden variables. The observed variables are molded as linear combinations of potential factors including the error terms. Information attained regarding interdependence between observed factors can later be utilized to reduce the set of variables within a dataset. Factor analysis originated in psychometrics and is applied in behavioral sciences operations research and applied sciences which deal with large quantities of data. In psychology, factor analysis is in most cases associated with intelligence search. Factor analysis has been used to search for factors within a broad range of spheres such as character, beliefs and attitudes. Factor analysis isolates the underlying variables that make clear the data. There are two types of factor analysis; principal factor analysis and common factor analysis. The factors generated by principal factor analysis are theoretical as being as liner combinations of variables whereas those generated by common factor analysis are theoretical latent variables. Computationally, the main difference is that the diagonal relationship matrix is substituted with common variables in common factor analysis. Factor analysis is performed through examining the pattern of connection between the observed variables. Variables which are highly related have a likelihood of being influenced by factors such as those which are moderately unrelated and have a more likelihood of being influenced by different factors. Principal component analysis is the most widespread factor analysis. Principal factor analysis seeks for a linear combination of measures in such a way that the maximum difference is extracted form the measures. It then removes the difference and search for a second liner a combination that explains the maximum proportion of the remaining variance. Conducting a Confirmatory Factor Analysis The main purpose of a Confirmatory Factor Analysis is to establish the ability of a prearranged variable model to fit within an observed set of data. Among the normal uses of Confirmatory Factor Analysis include; establishing the weight of a single factor representation compares the ability of two differing models to account for the same set of data, test the significance of particular factor loading, test the connection between two or more factor loadings and also to evaluate the convergent and discriminate strength of a set of measures. Conducting a Confirmatory Factor Analysis The six stages involved include; Describing the factor model which is the first thing required to be done accurately to define the model one wants to test. This involves choosing the number of factors and defining the nature of loadings between measures and factors. The loading can be fixed at zero or any other constant number or allowed to vary within specified constraints. Collect the measurements through measurement of variables on same experimental units. Obtain a correlation matrix by getting the correlation between each of the variables. Fit the model into data by selecting a method to obtain the estimates of factor loadings which were free to vary. The normal model-fitting method is the Maximum likelihood estimation that needs to be used unless the measures serious lack multivariate normality. In such a case one can use Asymptotically distribution free estimation. Evaluation of model adequacy s done when the factor model is fit the data, the factor loading are selected to minimize the difference between the correlation matrix implied by the model and the actual observed matrix. The amount of difference after the best parameters have been selected can be used as a measure as to how reliable the reproduction is with the data. The commonly used assessment of model adequacy is the X2 goodness of fit test. Null hypothesis for this test holds that the model sufficiency for the data, while the other is that there a significant level f differences. Regrettably, this test is highly sensitive to sample size since, tests used in testing large samples generally lead to a rejection of null hypothesis, even when factor model is suitable. Other statistics like the Tucker-Lewis index, compare the fitness of planned model to a null representation.   These statistics show less sensitivity to sample size. By comparing these two models with other model one can is able observe the difference between their X 2 statistics which is almost equal to X2 distribution. About al individual factor loading tests can be compared to reduced and full factor models.   In situations where there is no comparison of full and reduced models, use of Root mean square error of approximation is recommended which is n estimation of discrepancy per degree of freedom within the model. References DeCoster, J. (1998). Overview of Factor Analysis. Retrieved on August, 16, 2010 from http://www.stat-help.co/notes.html

interview :: essays research papers

The family member that was interviewed was Erin. The relationship between the interviewer and the interviewee is third cousins through marriage. The interview took place in Erin’s apartment living room. Since she is an RA she lives in one of the apartments of Sara Tracy Dorm. When the interviewer walked into the room he could tell that she was very clean and rather sophisticated, just by the way her room was set up. The interviewee was sitting on her futon and was very alert. There were pink and yellow carnations on the table, which I found out that they are not real. Erin 20 years old and has an ethnic origin of Irish. Erin is a Caucasian and when asked what religion she was, Erin responded proudly â€Å"Catholic†. The next question to be asked was â€Å"what are you wearing?† and me not paying attention to the question read it allowed, when I could have just observed her to answer the question. But, she caught my slip up and she responded â€Å"nothing† and laughed sarcastically. In reality, she had on a older and faded WJU swimming t-shirt on with a pair of worn out jeans. She seamed happy and content, but when I asked â€Å"what is your mood today?† she said, â€Å"Alright, calm I guess†¦not too happy and not too sad.† Then I asked her about her attitude and she responded with â€Å"happy to be interviewed†.   Ã‚  Ã‚  Ã‚  Ã‚  Erin’s mom’s family is from New York, and her dad’s family is from West Virginia. She was born in San Diego, California, on August 10, 1984. Her family then moved to Connecticut when Erin was â€Å"just a wee lad† as she put it, so she does not remember a whole lot from that particular time period. Then after living in Connecticut for a couple of years her family moved to West Virginia where they are presently located now.   Ã‚  Ã‚  Ã‚  Ã‚  Erin has many of friends who are outgoing and not afraid to speak their mind. All of them are nice and funny. They know how to make a good time out of the worst days. Erin, however, is pretty much the brain of the operations that they carry out. During the interview Erin was sitting on her futon drinking a cup of coffee acting all sophisticated. She was really relaxed and was not fidgeting like I was, so she did not seem like she was nervous.

Physio Cardio Lab Report Answers Essay

1. Explain how the body establishes a pressure gradient for fluid flow. Pressure gradient is the flow rate of a liquid through a pipe. This is directly proportional to the difference between the pressures at the two ends of the pipe and inversely proportional to the pip’s resistance. The pressure gradient is directly dependent upon blood vessel radius which essentially controls blood flow. The bigger the blood vessel radius, the more blood flow or fluid flow. The smaller blood vessel radius, the lesson blood or fluid flow. 2. Explain the effect that the flow tube radius change had on flow rate. How well did the results compare with your prediction? Flow tube radius change has a direct effect on flow rate. As evidenced in this lab, when flow tube radius was increased, the flow rate was also increased. They are directly proportional. As evidenced from the text, when flow tube radius increases in a blood vessel, the flow rate is much more free flowing and flows a lot quicker as the radius is increased. When starting with 1.5mm of radius, the flow was very slow, yet when increased to 2mm, 3mm, and eventually to 5mm, the flow within the blood vessel incrementally increased. 3. Describe the effect that radius changes have on the laminar flow of a fluid. Laminar Flow is defined as the free-flowing blood in the middle of the vessel. Radius change is directly proportional on laminar flow. In a constricted vessel, proportionately more blood is in contact with the vessel wall and there is less laminar flow, significantly diminishing the rate of blood flow in the vessel, yet if the vessel is more dilated, or the radius is increased, more blood flow is able to get in, thus increasing the blood  flow. The bigger the radius, the more laminar flow of fluid. 4. Why do you think the plot was not linear? (Hint: look at the relationship of the variables in the equation). How well did the results compare with your prediction? If the variables are radius on the X-axis and flow rate on the Y-axis, the experiment called for the experimenter to incrementally increase the radius and plot the results. As we know, radius is directly proportional to flow rate in that as the radius increases so does the flow rate, therefore, the plotted graph has to be linear. If one increases, so does the other going in a straight line! Activity 2 Questions: 1. Describe the components in the blood that affect viscosity? The components in the blood that affect viscosity are the presences of plasma proteins and formed elements such as white blood cells (leukocytes), red blood cells (erythrocytes), and platelets. When these formed elements and plasma proteins in the blood slide past one another, there is an increase in the resistance to flow. 2. Explain the effect that the viscosity change had on flow rate. How well did the results compare with your prediction? Viscosity is defined as the thickness or stickiness of a fluid. In regards to flow rate, they are inversely comparable and thus as you increase viscosity or the â€Å"thickness† of the blood, the flow rate decreases. As seen in the graph, increasing the viscosity inversely decreases the flow rate each time you increased it by 1. 3. Describe the graph of flow versus viscosity. As evidenced in the graph, the constants in this experiment were radius,  length, and pressure. The variables were flow rate and viscosity. The y axis represented flow rate and the x axis represented viscosity. As viscosity increased, the flow rate decreased causing a linear or inverse curve relationship going down. 4. Discuss the effect that polycythemia would have on viscosity and on blood flow. Polycythemia is a condition in which excess red blood cells are present. We learned earlier that an increase in red blood cells results in an increase in blood viscosity. An increase in blood viscosity directly affects blood flow, in that blood flow would decrease. Thus, the presence of polycythemia would inversely affect blood flow rate by decreasing it. Activity 3 Questions: 1. Which is more likely to occur, a change in blood vessel radius or a change in blood vessel length? A change in blood vessel radius is more like to occur because blood vessel length only increases as we grow into maturity and in adulthood blood vessel lengths stay constant. The only possibility of blood vessel length changing is when we gain or lose weight. Through the process of vasodilation, or the smoothing of the blood vessel muscle, you can change the radius of the vessel more frequently. 2. Explain the effect that the change in blood vessel length had on flow rate. How well did the results compare with your prediction? Blood vessel length, when increased causes more friction or resistance thus making it more difficult for blood to flow through the vessel. In summation, increasing blood vessel length inversely effects flow rate but decreasing flow rate. My prediction was that an increase in blood vessel length would inversely effect blood flow. As evidenced in this experiment, with the increase of the blood vessel length, there was a decrease in blood flow. 3. Explain why you think blood vessel radius can have a larger effect on the body that changes in blood vessel length. In the blood flow equation (as seen to the right), blood flow is directly proportional to the fourth power of vessel radius. Dramatic changes happen in regards to blood flow because of small changes in blood vessel radius. The smaller the blood vessel radius, the greater the resistance. Blood vessel radius is the single most important factor in determining blood flow resistance. 4. Describe the effect that obesity would have on blood flow and why. As referenced from this experiment, weight, either gain or loss effects blood vessel length. A change in blood vessel length can only be altered through the gain or loss of weight. As evidenced in this experiment, when blood vessel length is increased as a result of weight gain, there is greater resistance or friction within the vessel making blood flow through that vessel more difficult thus decreasing blood flow. Obesity different effect blood flow in that, there are increased blood vessel lengths, causing greater friction or resistance within the vessel and a decrease in blood flow. Activity 4 Questions: 1. Explain the effect that pressure changes had on flow rate. How well did the results compare with your prediction. Pressure changes have a profound effect on flow rate. As pressure increases, flow rate also increases. They are directly proportional. In regards to my prediction, I predicted that as pressure increased, so would flow rate. 2. How does the plot differ from the plots for tube radius, viscosity, and tube length? How well did the results compare with your prediction. The plot for pressure in linear in that, an increase in pressure is directly proportional to flow rate. It was a perfectly straight line upwards as pressure increased. In regards to the plot for tube radius, it was very similar in that results were more curve shaped but went in the same directly upward. As vessel radius increased so did flow rate. In regards to viscosity, they were drastically different, as viscosity increased, the rate of flow decreased because there was more resistance. In regards to tube length, this is drastically different than pressure because with an increase in tube length, there is a decrease in rate of flow because there is more resistance within the vessel itself. After learning that vessel radius is the greatest factor in regards to flow rate, I predicted that with an increase in pressure there would also be an increase in flow rate. 3. Explain why pressure changes are not the best way to control blood flow. Pressure changes are not the best way to control blood flow because it could place more stress on the heart (which causes the initial pressure) and requires the heart to change its force of contraction. The blood vessels need time to respond to that change in force as well as the large arteries around the heart. It required for them to have more tissue in their tunics to accommodate the heart and it’s increase of force. Plus, the best way to control blood flow, as seen from these experiments is through increasing vessel radius. 4. Use you data to calculate the increase in flow rate in ml/min/mm Hg. In this experiment, radius, viscosity, and length remained constant, and pressure and flow rate were the variables. I started off with a pressure of 25 mm Hg and the flow rate was 35mm/min. As I increase the pressure by 25 mm Hg each time, the flow rate increased by about 35 mm/min each time. Activity 5 Questions: 1. Explain the effect of increasing the right flow tube radius on the flow rate, resistance, and pump rate. Increasing the right flow tube radius is directly proportional to increasing flow rate. As evidenced in other experiments, increasing tube radius decreases resistance thus increasing flow rate. In addition, as the right flow tube radius increased, so did the pump rate. Each time that I increased the right flow tube radius by .5mm, the pump rate increased as did the flow rate because of the decrease in resistance. 2. Describe what the left and right beakers in the experiment correspond to in the human heart. The left beaker represents the side of the heart where blood is pumped through the lungs to the opposite side of the heart. The right beaker represents the side of the heart that delivers blood to the system of the body. 3. Briefly describe how the human heart could compensate for flow rate changes to maintain blood pressure. The human heart compensates for flow rate changes by altering heart rate, stroke volume or resistance. If resistance decreases, heart rate can increase to maintain the pressure difference. If resistance is decreasing, there is an increase in flow rate. Activity 6 Questions: 1. Describe the Frank-Starling law in the heart. The Frank-Starling law in the heart refers to when more than the normal volume of blood is returned to the heart by the venous system. In this process, the heart is stretched which results in a more forceful contraction of the ventricles. This causes more than normal amounts of blood to be ejected by the heart which raises stroke volume. 2. Explain what happened to the pump rate when you increased the stroke volume. Why do you think this occurred? How well did the results compare with your prediction? When you increase the stroke volume, there is an inverse decrease in pump rate, even though there is a constant amount of flow that results. This is directly the opposite of my predictions, yet I learned that the reason why pump rate decreases when stroke volume increases is because the heart intrinsically alters stroke volume to accommodate changes in preload or during the period where the ventricles are stretched by the end diastolic volume. Stroke volume is also controlled by the strength and force of contractility of the heart. 3. Describe how the heart alters stroke volume? The heart alters stroke volume by altering the pump volume or the contractility. By altering the contractility, you are altering the strength of the cardiac muscle contraction and its ability to generate force. 4. Describe the intrinsic factors that control stroke volume. The intrinsic factors that control stroke volume are heart rate and cardiac output. Total blood flow is proportional to cardiac output. Thus, when the stroke volume decreases, the heart rate music increase to maintain cardiac output. Yet, when stroke volume increases, the heart rate must decrease to maintain cardiac output. Activity 7 Questions: 1. Explain how the heart could compensate for changes in peripheral resistance. The heart can compensate for changes in peripheral resistance by decreasing blood viscosity and through adjusting the force of contraction of the heart. Increasing contractility or forcing contraction of the heart combats afterload and blood flow resistance. Increasing contractility will increase cardiac output by increasing stroke volume. 2. Which mechanism had the greatest compensatory effect? How well did the results compare with your prediction? My prediction was that increasing the left flow tube radius would have the greatest impact in regards to blood flow into the right tube, but adjusting the force of contraction of the heart had the greatest compensatory effect on the flow of blood into the right beaker. 3. Explain what happened when the pump pressure and the beaker pressure were the same. How well did the results compare with your prediction? When the pump pressure and the beaker pressure were the same, the valve would not open because there was insufficient driving pressure to force fluid out of the pump. This was adverse to my prediction, where I predicted that there would be an increase of flow, but I was incorrect, in that nothing happened and there was no flow. 4. Explain whether it would be better to adjust heart rate or blood vessel diameter to achieve blood flow changes at a local level. I think that it would be better to adjust heart rate in order to achieve blood flow changes at a local level. Although the text and experiments have demonstrated that it is more effective to increase blood vessel diameter in order to increase the rate of flow within blood vessels, I think that exercise increases your heart rate which is directly linked to an increase in blood flow.

Chemical Structures Starting with the Letter V