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I understand the rationale that underpins representative sampling (i.e. to avoid bias so that the sample 'broadly' represents the target population). Suppose the size of the target population is 600 and the population comprises of four types of units as follows: 100 white units 250 black units 50 green units 200 yell...
Sorry if this is a newb question; I'm trying to teach myself statistics for the first time. I think I have the basic procedure down, but I'm struggling to execute it with R. So, I'm trying to evaluate the significance of regression coefficients in a multiple linear regression of form $$ \hat y = X \hat \beta$$ I think...
I have a data set of skewed nutrient intake values, from around 7800 individuals, of whom around 3000 had two measures of daily nutrient intake (the others only had one measure), so this is a repeated measures design, very unbalanced. The boxcox transformation in the MASS package in R identified a suitable lambda (0.4)...
Does anyone know of an R package or have a way to create phrase nets like this?
Whats the difference between a GLM model (logistic regression) with a binary response variable which includes subject and time as covariates and the analogous GEE model which takes into account correlation between measurements at multiple time points? My GLM looks like: Y(binary) ~ A + B1X1(subject id) + B2X2(time) ...
In the field of genome assemblies in biology (the problem being reconstructing the genome from many, short random pieces of it, where a genome is one or more long strings of a limited alphabet), there is a metric called 'N50' for a set of strings (pieces of DNA sequence). The N50 length is defined as 'the length of the...
I'm trying to perform Fisher's exact test in R. I'm calculating odds ratio like this $$\frac{(\text{no. of successes in my set}) \cdot (\text{no. of failures in background set})}{\text{(no. of successes in background set)} \cdot (\text{no. of failures in my set})}$$ In the denominator, I get 0 for some cases, because t...
I have a real-time domain where I need to assign an action to N actors involving moving one of O objects to one of L locations. At each time step, I'm given a reward R, indicating the overall success of all actors. I have 10 actors, 50 unique objects, and 1000 locations, so for each actor I have to select from 500000 p...
I have just read the answers to the question ...... Adding coefficients to obtain interaction effects - what to do with SEs? .......and found this really helpful! I am looking to do something similar in R, but I have slightly different sample sizes between groups. Can I still use the same equation to combine the two er...
I saw the Johnson family of distributions in context of reliability and demand modeling for supply chains, but I am not sure if they are bringing real benefit to pay for their relatively more complex format. What are their major features and when one should use them?
I have a problem consists of forecasting the next 16 values for 250 time series of daily demands, Can I forecast just for one period ahead and then multiple it by 16? is it correct? I was wondering if you give me your suggestions.
I'm looking to perform a kernel density estimation on a set of 40 locations. At first I used LSCV as the bandwidth, however it seems to have oversmoothed the data, creating high densities in areas it shouldn't. I've been looking around for information on which bandwidths are the best to use in which situations but am s...
I have a set of counts as a response variable (anywhere from 0 to 85). I want to find the easiest way to plot count on the y-axis vs frequency of that count on the x-axis, the type of plot you see in "power law" plots. For example, I have 2 people with count = 100, 5 people with count 75, ..., 20 people with count 5. T...
I'd like to fit a distribution (any you like) based on these requirements: Produces integer values (preferable but not required) Mean =100 Std=114 Quantiles( 25%, 50%, 75%)=(6,39,200) Min=0; Max=~300 (but $\infty$ is acceptable); Poisson fits criteria 1,2 and nearly 3, but not 4 by far. Lognormal... maybe EXTRA info:...
Is anyone familiar with quantile normalization? As I understand it's a way to "polish" a set of datasets so that they have the same "statistical properties" (according to Wikipedia)? I wonder if anyone knows what are the statistical properties that they refer to when they say quantile normalization is a technique for...
Given a set of data like this: x y1 y2 50 102.50 16 100 408.60 64 200 1,871.30 256 400 8,824.40 1024 800 49,695.60 4096 My hypothesis is that when x doubles, you should find that y quadruples. I believe this is equivalent to saying that x is proportional to the sq...
Suppose you have a multiple level categorical variable $x$ (4 levels so 3 dummy variables) and you are doing a multiple linear regression against $y$ (some outcome variable). If the F test is significant does that mean at least one of the level of $x$ is linearly associated with $y$? Or does it mean that $x$ is associa...
I need help figuring out the correct way to calculate winners at our science fair. I don't want my ignorance of statistics & math to get in the way of a kid's chances of winning. (lots of scholarship & advancement benefits at stake). Thanks in advance for your help. First a little background of how we have things set u...
Following the question here, the target population is made up of 600 units which are distributed as follows: while units (17%) black units (42%) green units (8%) yellow units (33%) A representative sample would be one which broadly reflects this percentage distribution. However, in this case, one would end up with on...
Currently I have a data set which are known to belong to two classes, and would like to build a classifier using SVM. However, there exist different confidence levels for this data set. For example, for some data points, we are very certain that they belong to class 1; while for some data points, we think they should ...
We have the standard linear multivariate regression model $y=\beta_0+\beta_1x_1+\beta_2x_2+u$ under the Gauss-Markov assumptions. Suppose we estimate $\gamma_0, \gamma_1, \gamma_2$ from $x_2=\gamma_0+\gamma_1x_1+\gamma_2y+v$ and get $\hat{\gamma_0}, \hat{\gamma_1}, \hat{\gamma_2}$. Is $\frac{1}{\hat{\gamma_2}}$ an unbi...
If I have a set of samples, say 100-200 samples and I'd like to create the distribution model from this list of samples, what is a reasonably efficient way of doing it? Are there any opensource / easily accessible statistical libraries? eg: if I assume it's a normal distribution, I can easily find the mean and variance...
I have two sets of data: the bacteria count on people's hands (n=1e4) without washing x. They then washed their hands and the count was made again xwash. What is the best way to estimate the reduction between these groups? Is there a formalised/sophisticated comparison test or am I reduced to hypothesis testing? W...
I am struggling to understand full column rank vs. full row rank to estimate parameters of multivariate regression case. When do we use row rank, and when do we use column rank?
I have a matrix X where the rows denote the cases and the columns the variables. I use a standard row-metric preserving biplot in order to represent the cases in a subspace. If I wanted to add a supplementary point (i.e. a row) I can simply project the point it into that space. But, how can I optimally fit a point into...
I take a SRS sample of size n from a population of x values ranging from 1 to N. Each selected unit also has a probability p of success or q = 1-p of failure (i.e. the probability of success/failure is independent of the value of x). What is the expected value of the minimum x value for which success occurs? I believe ...
I was trying to find out whether an oversampling can really make a model better. On this blog page, it says that it can improve a decision tree, but it shouldn't improve a logistic regression. Quotation below: Standard statistical techniques are insensitive to the original density of the data. So, a logistic regressio...
I am trying to get to grips with Clustering and Visualisation. I have a set of data (a matrix) that I want to cluster (using R) and then visualise (HTML5 Canvas). So, I can use MDS to get the coordinates of a matrix, for example: cells <- c(1, 1, 2, 1, 4, 3, 5, 4) rnames <- c("A", "B", "C", "D") cnames <- c("X", "Y")...
I would like to test a proprietary method of financial time series prediction that says, in effect, that on a certain day/week in the future, to an accuracy of +/- 2 to 3 days/weeks, a financial time series will make a relative high or low on this predicted date, and furthermore, within a defined period in the future t...
I have a data consists of three independent variables and dependent variable, I want to fit a model to these data, p=f(x1,x2,x3), how can I find the best fit for these data? it might be linear, quadratic,... could you please guide me to find the optimum way to find the model.
We have a potential biomarker for predicting whether a patient has cancer or not. The biomarker test result is binary being positive or negative. We want to get some sense of the amount of patients that need to be tested to determine whether this biomarker is a good predictor or not. From reading on the internet it se...
Please help! I have recently been criticized for using pairwise comparisons to explain all three levels of a factor within a negative binomial GLM rather than all levels at once. I was told that it is "long-winded" and "uneccessary". I was under the impression that in GLMs one cannot bulk all levels of a factor togethe...
I would like to calculate the value of bacteria on 4 surfaces $i=\{1..4\}$. A person touches some of those 4 surfaces at random and a count is made on their finger after each surface contact ($x_i$). Someone lost the bacteria count ($x_i$) after each surface but I do know the total count (X) on a persons's finger afte...
I have a time series that follow an MA(1) process , I do non-overlapping aggregation with aggregation level $m=2,3,\dots$, and then I calculate autocorrelation of basic and aggregated series, for negative value of moving average parameter, aggregated autocorrelation becomes close to zero, means that the aggregated seri...
For tree based modeling most packages use some data element as the dependent variable. In uplift modeling the goal is to maximize the difference between treatment and control groups. One way to implement this is with a CART which maximizes the t-statistic for an interaction term between the split (1 = left, 0 = right)...
I am looking for alternatives to the kappa to assess inter-rater agreement. I've come across two hopefulls: Gwet’s AC1 statistic and PABAK. I wondered what the advantages and disadvantages of each were?
There are several packages that can apply the Durbin-Watson test for serial correlation. However, I do not see a package that supports the calculation in the case that once has a GLS weighted regression. For example, CRAN package lmtest notes in their changelog that they explicitly do not support weighted regressions (...
I am new to modeling with neural networks, but I managed to establish a neural network with all available data points that fits the observed data well. The neural network was done in R with the nnet package: require(nnet) ##33.8 is the highest value mynnet.fit <- nnet(DOC/33.80 ~ ., data = MyData, size = 6, decay...
Given a data matrix like this: [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 9.520 11.137 16.576 18.225 20.576 25.861 NA [2,] 9.005 9.491 11.106 16.530 18.184 20.495 25.773 [3,] 9.437 11.050 20.393 25.711 NA NA NA [4,] 9.442 11.058 20.411 25.711 NA NA NA [5,] 9.431 1...
I recently re-ran a survey for year to year comparisons. In the recent survey I changed the Likert scale slightly by anchoring each box rather than just # 1 and # 6. In other words, my scale went from this: 1 - agree completely, 2 , 3 , 4 , 5 , 6 - disagree completely To this: 1 - agree completely 2 - agree 3 - ...
I have been tinkering with an idea today, but I have only taken one semester of statistics, so please bear that in mind. Thanks. First up, the question: How do you judge multiple estimates (with standard errors included)? I don't mean estimating their mean or distribution, rather some representation of similarity. Some...
I'm reviewing a conference paper (not a stats conference). The authors have done some funny things with their methodology. The experiment setup has 4 treatments, each applied to the same 30 subjects. This is repeated in 10 different circumstances. ANOVA is used to determine whether the choice of treatment has any effec...
Suppose I have two models $A$ an $B$ that predict class labels. If these give binary predictions, these will appear as pairs of (false positive rate, true positive rate) in the ROC space. We should be able to construct different models to achieve any tpr and fpr along the linear interpolation of these curves by assigni...
Sample size can be calculated in different ways, for instance, using a margin of error and confidence level or doing power analysis etc. What would be some matters to take into consideration when choosing a method of sample calculation?
Ratios of two normally distributed variables (e.g X/Y) have no moments (e.g. means and variances) because Y can have zero values. However, lognormal variables have no zero values. How can I calculate the mean and variance of the ratio of two lognormal variables?
The correlation between two ratios with the same denominators are spurious. Similarly, the correlation between two mathematically-coupled variables could also be spurious. Are mathematically-coupled variables (e.g. age and income are used to derive two formulas, which are then used as Y and X in linear regression analy...
Many textbooks and papers said that intercept should not be suppressed. Recently, I used a training dataset to build a linear regression model with or without an intercept. I was surprised to find that the model without an intercept predicts better than that with an intercept in terms of rmse in an independent validati...
I'm working with multiple time series signals ${\{X_i\}}$ and one method to remove suspected noise is with PCA. But unlike most methods which remove the components with least variance, we remove much more substantial components (often the second or third). This is often done because empirically it's been shown to imp...
I've read several articles about how to perform Weibull distribution but they all did it with wind speed data in a time series manner (example: recorded data every 10mins and then averaged to every hour). My prob is that I've got only mean monthly wind speed for a year (from January to December). So how should I deal w...
How do I work out an adequate/representative sample in the following scenario? My intention is to use correlation and regression models to test the relationship between income level and money spent on a particular product by store type. Scenario There are 200 stores, with a total of 10,000 registered customers. The st...
I'm analyzing a data base from an ecological study and I'd like to read a good reference book about this kind of studies as there are some limitations concerning their analysis; for example, they are susceptible to ecological fallacy.
Can anyone please tell me what the alternative argument is in fisher.test() in R? What do greater and less imply? fisher.test(x, y = NULL, workspace = 200000, hybrid = FALSE, control = list(), or = 1, alternative = "two.sided", conf.int = TRUE, conf.level = 0.95, simulate.p.value = F...
I have the following variables: weight (ratio scale) result obtained from psychological test (eg. iq) (ratio scale) style1 (ratio scale) style2 (ratio scale) style3 (ratio scale) I want to test this hypothesis: People with high result on style 1 and high result on IQ scale are having bigger weight than people with h...
I am trying to expand my knowledge of statistics. I come from a physical sciences background with a "recipe based" approach to statistical testing, where we say is it continuous, is it normally distributed -- OLS regression. In my reading I have come across the terms: random effects model, fixed effects model, marginal...
I have just run a NBGLM and want to know something. If I am aiming to drop the least significant explanatory variables until all explanatory variables are significantly correlated wih the response variable (i.e. model selection finding the strongest variables). What do I do when there is a factor within the model that ...
I am trying to test a hypothesis I have about consolidation in the real-world market for a certain machine. (My apologies in advance for obfuscating a bit here, but some of the data is proprietary and may not be redistributed.) 1) The market has two components: new machines sold and existing machines in use. Companies ...
I have posted this question before but wanted to give a more thorough explanation of my problem so as to hopefully garner some assistance. I am also posting it on Talk Stats under the same title. I have a mutiple regression model with over 10,000 records and though the model has an R^2 of 91%, the lack of fit tests and...
Many machine learning algorithms, for example neural networks, expect to deal with numbers. So, when you have a categorical data, you need to convert it. By categorical I mean, for example: Car brands: Audi, BMW, Chevrolet... User IDs: 1, 25, 26, 28... Even though user ids are numbers, they are just labels, and do not ...
I would like to do model selection for generalized estimating equations (GEE). Pan (2001) is most frequently cited for developing a method using QIC. I am wondering if anyone knows of a way to do this in R? I am currently using the package 'geepack' for my GEE analysis. I heard about 'yags' but it is not available for ...
I'm currently doing some large correlational analysis: Let's just say I wanted every kendall-correlation and it's associated p-value from 20x30 Items in a neat matrix - should I be doing p-value adjustment correcting for multiple comparisons, eg. holm (nothing's significant) or should I just use the passthrough option ...
I have a basic demand series that follow MA(1) process,I've applied non-overlapping aggregation approach and then SES on both basic and aggregated series to obtain forecasts, and then I disaggregated forecasts resulted from aggregated series and finally I calculate ratio of MSEbasic/MSEdagg, where MSEbasic=Var(dt-ft) a...
I have count data for events measured within each of multiple individuals. However, the amount of time over which each individual was observed varies. Normally, if the counts were obtained over equal amounts of time, I'd do something like: fit = lmer( data = my_data , formula = count ~ (1|individual) , fami...
How, if at all, can one compare the "fit" of a simple linear vs. non-linear regression model to observed data? I apologize if I didn't search long/hard enough for the answer, but I cannot find anything concrete. -Patrick
I have to find the similarity between a reference document and a set of documents in a repository . Here is my method : 1. I find the term document matrix for all the documents including the reference document. 2. The svd is calculated for this matrix. 3. I take the v array (the third result). 4. I transpose this mat...
I'm clustering a set of data but I don't have truth document that allow me to evaluate the result of clustering (I have unlabelled data), so I can not use an external evaluation measure. In this case, is there any efficient evaluation measures - internal cluster validity measures, that will allow me to incrementally ev...
*Background:* I am doing an academic study that is more exploratory in nature (my advisor did not want me to develop any hypothesis). So I read books and conducted interviews to try and gather a large list of items that people feel are important and influential to the topic being studied. From that list, I developed th...
Please pardon my ignorance, but... I keep finding myself in a situation, where I'm faced with a bunch of new data I managed to find. This data usually looks something like this: Date Number1 Number2 Category1 Category2 20120125 11 101 Dog Brown 20120126 21 90 Cat Blac...
I am conducting three-way ANOVA (A*B*C) with 2 levels each. 1) I found A*B interaction. 2) I moved to 2-way ANOVA (A*B) and found interaction again. I reported Eta-squared and equivalent Cohen's d. 3) I moved to 1-way ANOVA (a1,a2,b1,b2) with mushed cells and bonferonni posthoc showed that b2 was lower than the a1,a2, ...
I am looking for a R command to test the difference of two linear regressoon betas. Lets say I have data $x_1, x_2...x_{n+1}$. $\beta_1$ is obtained from regressing $x_1$ to $x_n$ onto $1$ to $n$. $\beta_2$ is obtained from regressing $x_2$ to $x_{n+1}$ onto $1$ to $n$. Is there a way in R to test whether $\beta_1$ and...
Structural equation models (sem) are used to model latent variables. Renal function is a latent variable measured by serum creatinine levels (with measurement errors) expressed by many different clinical formulae derived from linear regression models. Inulin clearance is a gold standard for renal function. However, hun...
From StatSoft, Inc. (2013), Electronic Statistics Textbook, "Naive Bayes Classifier": To demonstrate the concept of Naïve Bayes Classification, consider the example displayed in the illustration above. As indicated, the objects can be classified as either GREEN or RED. My task is to classify new cases as they a...
I'm trying to find the probability of getting 8 trials in a row correct in a block of 25 trials, you have 8 total blocks (of 25 trials) to get 8 trials correct in a row. The probability of getting any trial correct based on guessing is 1/3, after getting 8 in a row correct the blocks will end (so getting more than 8 in...
The web-based company I work for has a system that receives packets of information from external sites. I would like to know what approaches can be used to identify patterns or associations between the external sites. For example site A sends a packet on subject 1. Shortly after many other sites may send through pac...
Following the question here, Probability Proportional to Size (PPS) Sampling Method seems appropriate in constructing a sample when the primary units are of different sizes in the target population. As I understand, this is a self-weighting technique, so does not require any special consideration in the data analysis s...
I would like to determine the effect of AGE or equivalently "time" on a continuous outcome variable while controlling for gender. I have repeated measures data across 6 time points. In order to take into account the correlation of the repeated measures, I am thinking of using a random slops/random intercepts model m...
I would like to understand how do the Boruta package work. Could you suggest some references for the theoretical aspect of so-called random forests? Below are two illustrative examples of why am I attracted by the Boruta algorithm. First example: > set.seed(666) > # simulates data > # y does not depend on x4 > # y dep...
I've got a dataset that I'd like to model, and it seems like the best model would be of the form: $y = (\beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3) \cdot (\beta_4 x_4 + \beta_5 x_5 + \beta_6 x_6) + \epsilon$. The $\beta_4$ through $\beta_6$ are independent of each other and have a linear effect on $y$ once modulated by th...
I have a Java code that performs a linear regression on a set of data using the Gauss-Jordan elimination. It calculates a linear, quadratic and cubic functions using the least squares method. My problem is choosing a function out of the three that best models my data. This is ofcourse, without plotting the curve. So le...
I'm trying to measure the reverberation so to speak of a variable - and its effect on itself in the subsequent units of time and its effect on other variables. For example var1 will have an event where it generates 20 units on day one. I'd like to analyze what happens to var1 on day two, day three, and so on. But als...
I had this example in my machine learning lecture. Let $X_2,\ldots,X_n$ be identically distributed (but not independent) copies of $X_1$ drawn from $\mathcal N(0,1)$. Then $X_n$ converges to $Y = -X_1$ as $n \rightarrow \infty$. There isn't any explanation for why this sequence of random variables converges to $Y$. ...
The mean and variance of the folded normal distribution are known. Consider now the distribution of $(|x_1|, \ldots, |x_n|)$, where $\mathbb{x} \sim N(\mu, \Sigma)$. The mean of the multivariate folded normal distribution is easy to obtain. But what about the variance? I could not find references, and the calculation s...
Suppose I am building a predictive model where I am trying to predict multiple events (for instance, both the roll of a die and the toss of a coin). Most algorithms that I am familiar with work with only one target, so I'm wondering if there is a standard approach to this sort of thing. I see two possible options. Pe...
The margin of error is driven by the size of the sample. In a consultant's report (which is confidential at this stage), they collected responses from 10 store managers (out of a total of 200 store managers i.e. target population) and went on to make statements such as "only 20% of the respondents were happy with the s...
I have a time series of data with N=14 counts at each time point, and I want to calculate the Gini coefficient and a standard error for this estimate at each time point. Since I have only N=14 counts at each time point I proceeded by calculating the jackknife variance, i.e. $\operatorname{var}(G) = \frac{n-1}{n} \times...
I am trying to determine if there is a dependency between two survey questions about the effectiveness of a subject-specific online communities. The first survey question asks how frequently a user posts questions or comments. The second survey question asks if the participating in the community increases the user's ...
I have been reading about the delta method in regards to auto regressive distributed lag models. This is very new to me, so excuse any beginner mistakes. The problem is as follows: We have a model for gasoline consumption. $g$ is the per capita consumption, $y$ disposable income, $p$ is price, $g_{t-1}$ is lagged consu...
I am creating a program to collect and analyze prices for goods and alert the user when the price decreases so that they can buy it on "sale." I know a little statistics (e.g. standard deviation) but am looking for the best way to determine if a price drop is significant compared to historical prices - i.e. if I should...
I have 2 groups: N=350 (G1) and N=1,500(G2). G1 refers to 1 company and G2 is a group of 4 companies. Is z test appropriate to test the significant differences between percentage distribution?, i.e. if 51/49% male/female in G1 is significantly different than 46%/54% male/female in G2? Thanks!
For classifiers with binary outputs, their performance is summarized by a true positive rate and false positive rate. To interpolate the performance between two classifiers $A$ and $B$ with their respective (true positive rate, false positive rate) being $(t_A, f_A)$, and $(t_B,f_B)$, we can construct a new classifier ...
I have a question about something that my statistics teacher said about the following problem: There are two hospitals named Mercy and Hope in your town. You must choose one of these in which to undergo an operation. You decide to base your decision on the success of their surgical teams. Fortunately, under the new he...
Please note: I posted this first on Mathoverflow. Someone there advised me that on stats.stackexchange the question might fit better here. This is the link to the original post. I currently have to fit some heavy-tailed data. As the fitted (positive, continuous) distributions will be used in a numerical integration pro...
As far as I understand, the Minimum Covariance Determinant (MCD) estimator looks for the subset of h data points whose covariance matrix has the smallest determinant. the Minimum Volume Ellipsoid (MVE) searches for the ellipsoid with the smallest volume that covers h data points. Once either subset is found, the rob...
I've implemented the classic HMM model from Rabiner's tutorial for gesture recognition and it has worked well. Now, I'm trying to implement the HMM Threshold Model which calls for an HMM with null transitions. Null transitions do not provide any output symbols and the threshold model has 2 states which are connected t...
I am reading P.R. Rosenbaum, Model-based direct adjustment, Journal of the American Statistical Association, 1987 (82), pp. 387-394. However, there is one equation, which I can't understand. $$ d = \frac{1}{N}\{\sum_{s=1}^{S}\sum_{i=1}^{N_s}\frac{z_{si}r_{si}}{\hat{e}_s} - \sum_{s=1}^{S}\sum_{i=1}^{N_s}\frac{(1-z_{si}...
First time post and I'm not sure if I'm posting in the right place but here goes: I enjoy Sports and was reading a book over Christmas (Mathletics by Wayne Winston) and to cut a long story short have started ranking sports teams based on least Squares Regression (based on the number of points scored or conceded) to gen...
I have some survey response data that are inconsistent and I'm not sure what is the best way to handle them. This is the nature of the inconsistency: Have you ever had a food poisoning episode that you think might have been caused by the food in a particular restaurant ? a) Yes b) No Did any of these episodes preven...
The Minimum Covariance Determinant (MCD) estimator may be used to achieve robustness when estimating a covariance matrix. It looks for the subset of $h$ data points (out of $n > h$) whose covariance matrix has the smallest determinant and it computes the covariance of those $h$ points. Why does minimising the determina...
I'm trying to predict the gender of French nouns based on their suffixes. I have a corpus of 10k nouns. For each noun, I split the root from the suffix. I create five instances but with varying suffix lengths: 1, 2, 3, 4 and 5. The class name I'm assigning to each instance is composed of the gender and the length of th...
I have asked following questions before More than one outcome (dependent) variables in ordinal logistic regression How to handle more than one dependent variable (categorical) in logistic regression? Using Rasch model to explain relationships between a set of dependent and independent variables Use of further analysis ...
Suppose the target population is a group of 11 company CEOs and 7 CEOs responded to a question about their level of annual bonus on a 7 point Likert scale. The responses are as follows: 7, 7, 7, 7, 7, 7, and 5. The average response score then is 6.71. If the last two levels of the Likert scale are '6 = satisfied' and ...