Generalized linear Modelling and Survival Analysis Assignment HelpGeneralized modelling and survival analysis are two popular topics in statistics. They deal with the concepts of ANOVA, maximum likelihood estimation and R programming, among other related concepts. Statisticsassignmentexperts.com is a one-stop-shop for all statistics assignment help. Our online experts are well-versed with all these advanced topics in statistics. They cater to an array of problems faced by students who need generalized modelling and survival analysis assignment help.
What is Generalized Linear Modelling?The general linear model (GLM) is conventional linear regression models that are used for continuous response variable with categorical or/and continuous predictors. Examples include ANCOVA (with fixed effect only), ANOVA and multiple linear regression. On the other hand, the term generalized linear model, popularized by McCullagh and Nelder (1982, 2nd edition, 1989), refers to a larger class of models which include Poisson regression, ANOVA, and log-linear models among others. Our online statistics tutors have crafted the table below that provides a good summary of generalized linear models.
|Multinomial response||Multinomial||Generalized Logit||Mixed|
- Random component
- Systematic component
- The Link function
Assumptions in generalized linear models
All cases are independent. Data (Y1, Y2… Yn) are distributed independently.
It is not a must for the dependent variable to be normally distributed
There is no linear relationship dependent and independent variables in GLM. However, the explanatory variables and transformed response in terms of the link function exhibit a linear relationship.
Homogeneity of variance does not have to be met
Errors should not be normally distributed but independent
GLMs use maximum likelihood estimation (MLE) instead of ordinary least squares when estimating parameters
Sufficiently large samples determine the goodness-of-fit
Get a more detailed discussion on these assumptions by getting our statistics homework help. Also, our professional statistics assignment helpers recommend the following books: Agresti(2007), Agresti(2013), and McCullagh & Nelder(1989).
Learn more about Survival Analysis
Survival analysis refers to approaches in statistics used to investigate the time it takes an event of interest to happen. This analysis is applied in a variety of field such as:
Cancer studies – study patients’ survival time
Sociology - analysis of the history of events
Engineering – failure-time study
The following two related functions are used model and describe survival data:
The survivor function or the survival probability – It represents the probability of an individual surviving from the time of origin to an unknown beyond time The Kaplan-Meier is denoted by S(t) and is a method usually used to estimate this time. Also, the researcher can use the Log rank test can be used to test survival curves differences among groups.
The hazard function – This function gives an instantaneous potential of the event occurring at a time. The hazard function is a primary diagnostic tool. It can be used to specify a mathematical model for survival analysis. The hazard function is denoted by h(t)
The Kaplan-Meier Survival estimate
This is a non-parametric approach used to estimate the survival probability from observed survival times. Kaplan and Meier created it in 1958. The Kaplan-Meier's function only changes value at the time of each event. The KM survival curve can be drawn by plotting the survival probability against time. The graph can be used to prepare a useful summary and estimate measures such as median survival time.
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- Introduction; Background review of linear modelling and survival analysis, model assessment, linear models in matrix notation and many more
- Exponential family distributions; including definitions and relevant examples, mean and variance, and variation function and scale parameter
- Generalized linear models; Link function, linear predictor, canonical link, deviance, Pearson residuals, significance of parameter estimates, Fisher scoring algorithms, iterative reweighted least squares, and maximum likelihood
- Normal linear regression models; variance analysis, least squares, factor interaction between factor, and orthogonality of parameters.
- Binomial and binary data analysis; distribution of models, odds ratio, logistic regression models, one and two-way regression analysis
- Poisson count data analysis; log-linear models, Poisson regression models with offset, and two-dimensional contingency tables
- Survival data; hazard cumulative and function, the survivor, Kaplan-Meier estimate of the survivor function
- Weibull distribution to survival data and fitting exponential; hazard plots and cumulative hazard plots
- PH regression and proportional hazards cox; model fitting and diagnostics, assumptions and interpretation and, confidence intervals and hazard ratios
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