I have a dependent variable Y= Number of complete months a child was breastfed together with some independent variables X1,X2,X3. Colleagues suggest time series models/ multiple linear regression/Logistic regression(after categorizing). From my point of view, I believe Poisson/negative binomial regressions are appropriate since this is like a count data.
Which model do you think I should run? Please, provide literature if there is any?
Related
I'm working on a simple project in which I'm trying to describe the relationship between two positively correlated variables and determine if that relationship is changing over time, and if so, to what degree. I feel like this is something people probably do pretty often, but maybe I'm just not using the correct terminology because google isn't helping me very much.
I've plotted the variables on a scatter plot and know how to determine the correlation coefficient and plot a linear regression. I thought this may be a good first step because the linear regression tells me what I can expect y to be for a given x value. This means I can quantify how "far away" each data point is from the regression line (I think this is called the squared error?). Now I'd like to see what the error looks like for each data point over time. For example, if I have 100 data points and the most recent 20 are much farther away from where the regression line/function says it should be, maybe I could say that the relationship between the variables is showing signs of changing? Does that make any sense at all or am I way off base?
I have a suspicion that there is a much simpler way to do this and/or that I'm going about it in the wrong way. I'd appreciate any guidance you can offer!
I can suggest two strands of literature that study changing relationships over time. Typing these names into google should provide you with a large number of references so I'll stick to more concise descriptions.
(1) Structural break modelling. As the name suggest, this assumes that there has been a sudden change in parameters (e.g. a correlation coefficient). This is applicable if there has been a policy change, change in measurement device, etc. The estimation approach is indeed very close to the procedure you suggest. Namely, you would estimate the squared error (or some other measure of fit) on the full sample and the two sub-samples (before and after break). If the gains in fit are large when dividing the sample, then you would favour the model with the break and use different coefficients before and after the structural change.
(2) Time-varying coefficient models. This approach is more subtle as coefficients will now evolve more slowly over time. These changes can originate from the time evolution of some observed variables or they can be modeled through some unobserved latent process. In the latter case the estimation typically involves the use of state-space models (and thus the Kalman filter or some more advanced filtering techniques).
I hope this helps!
I am trying to predict the statistically significant variables out of a list of binary variables. I am having a conceptual doubt in the below mentioned 2 approaches to find the relevant variables.
Dependent variable:
Height of a person
Independent variables:
Gender(Male or Female)
Financial_Status(Below Poverty Line or not)
College_Graduate(Yes or No)
Approach 1: Fitting a linear regression while taking these as dependent/independent variables and finding the statistically significant variables
Approach 2: Performing an individual statistical test for each dependent variable(t-test or some other relevant test) to compute the statistically significant variables
Are both of these approaches similar and will give similar results? If not, what's the exact difference?
Since you have multiple independent variables, than clearly no.
If you would like to go for the ttest approach for each of the values of the different independent variables (Gender, Financial_Status and College_Graduate) then it means you'll perform 3 different tests. Performing multiple tests is something that is risky in terms of false positive results, and thus should be adjusted with a multiple comparison adjustment method (Bonferoni, FDR, among others).
On the other hand, if you'll use a single multiavariate linear regression you wouldn't have the correct for multiple comparisons, which is why, in my opinion, is the better approach.
I am writing a study protocol for my masters thesis. The study seeks to compare the rates of Non Communicable Diseases and risk factors and determine the effects of rural to urban migration. Sibling pairs will be identified from a rural area. One of the siblings should have participated in the rural NCD survey which is currently on going in the area. The other sibling should have left the area and reported moving to a city.Data will collected by completing a questionnaire on demographics, family history,medical history, diet,alcohol consumption, smoking ,physical activity.This will be done for both the rural and urban sibling, with data on the amount of time spent in urban areas fur
The outcomes which are binary (whether one has a condition or not) are : 1.diabetic, 2.hypertensive, 3.obese
What statistical method can I use to compare the outcomes (stated above) between the two groups, considering that the siblings were matched (one urban sibling for every rural sibling)?
What statistical methods can also be used to explore associations between amount spent in urban residence and the outcomes?
Given that your main aim is to compare quantities of two nominal distributions, a chi-square test seems to be the method of choice with regard to your first question. However, it should be mentioned that a chi-square test is somehow "the smallest" test for answering differences in samples. If you are studying medicine (or related) a chi-square test is fine because it is also frequently applied by researchers of this field. If you are studying psychology or sociology (or related) I'd advise to highlight limitations of the test in the discussions section since it mostly tests your distributions against randomly expected distributions.
Regarding your second question, a logistic regression would be applicable since it allows binomial distributed variables both for independent variables (predictors) and dependent variables. However, if you have other interval scaled variables (e.g. age, weight etc.) you could also use t-tests or ANOVAs to investigate differences between these variables with respect to the existence of specific diseases (i.e. is diabetic or not).
Overall, this matter strongly depends on what you mean by "association". Classically, "association" refers to correlations or linear regression (for which you need interval scaled variables on "both sides") but given your data structure, the aforementioned methods possess a better fit.
How you actually calculate these tests depends on the statistics software used.
I have a trading strategy on the foreign exchange market that I am attempting to improve upon.
I have a huge table (100k+ rows) that represent every possible trade in the market, the type of trade (buy or sell), the profit/loss after that trade closed, and 10 or so additional variables that represent various market measurements at the time of trade-opening.
I am trying to find out if any of these 10 variables are significantly related to the profits/losses.
For example, imagine that variable X ranges from 50 to -50.
The average value of X for a buy order is 25, and for a sell order is -25.
If most profitable buy orders have a value of X > 25, and most profitable sell orders have a value of X < -25 then I would consider the relationship of X-to-profit as significant.
I would like a good starting point for this. I have installed RapidMiner 5 in case someone can give me a specific recommendation for that.
A Decision Tree is perhaps the best place to begin.
The tree itself is a visual summary of feature importance ranking (or significant variables as phrased in the OP).
gives you a visual representation of the entire
classification/regression analysis (in the form of a binary tree),
which distinguishes it from any other analytical/statistical
technique that i am aware of;
decision tree algorithms require very little pre-processing on your data, no normalization, no rescaling, no conversion of discrete variables into integers (eg, Male/Female => 0/1); they can accept both categorical (discrete) and continuous variables, and many implementations can handle incomplete data (values missing from some of the rows in your data matrix); and
again, the tree itself is a visual summary of feature importance ranking
(ie, significant variables)--the most significant variable is the
root node, and is more significant than the two child nodes, which in
turn are more significant than their four combined children. "significance" here means the percent of variance explained (with respect to some response variable, aka 'target variable' or the thing
you are trying to predict). One proviso: from a visual inspection of
a decision tree you cannot distinguish variable significance from
among nodes of the same rank.
If you haven't used them before, here's how Decision Trees work: the algorithm will go through every variable (column) in your data and every value for each variable and split your data into two sub-sets based on each of those values. Which of these splits is actually chosen by the algorithm--i.e., what is the splitting criterion? The particular variable/value combination that "purifies" the data the most (i.e., maximizes the information gain) is chosen to split the data (that variable/value combination is usually indicated as the node's label). This simple heuristic is just performed recursively until the remaining data sub-sets are pure or further splitting doesn't increase the information gain.
What does this tell you about the "importance" of the variables in your data set? Well importance is indicated by proximity to the root node--i.e., hierarchical level or rank.
One suggestion: decision trees handle both categorical and discrete data usually without problem; however, in my experience, decision tree algorithms always perform better if the response variable (the variable you are trying to predict using all other variables) is discrete/categorical rather than continuous. It looks like yours is probably continuous, in which case in would consider discretizing it (unless doing so just causes the entire analysis to be meaningless). To do this, just bin your response variable values using parameters (bin size, bin number, and bin edges) meaningful w/r/t your problem domain--e.g., if your r/v is comprised of 'continuous values' from 1 to 100, you might sensibly bin them into 5 bins, 0-20, 21-40, 41-60, and so on.
For instance, from your Question, suppose one variable in your data is X and it has 5 values (10, 20, 25, 50, 100); suppose also that splitting your data on this variable with the third value (25) results in two nearly pure subsets--one low-value and one high-value. As long as this purity were higher than for the sub-sets obtained from splitting on the other values, the data would be split on that variable/value pair.
RapidMiner does indeed have a decision tree implementation, and it seems there are quite a few tutorials available on the Web (e.g., from YouTube, here and here). (Note, I have not used the decision tree module in R/M, nor have i used RapidMiner at all.)
The other set of techniques i would consider is usually grouped under the rubric Dimension Reduction. Feature Extraction and Feature Selection are two perhaps the most common terms after D/R. The most widely used is PCA, or principal-component analysis, which is based on an eigen-vector decomposition of the covariance matrix (derived from to your data matrix).
One direct result from this eigen-vector decomp is the fraction of variability in the data accounted for by each eigenvector. Just from this result, you can determine how many dimensions are required to explain, e.g., 95% of the variability in your data
If RapidMiner has PCA or another functionally similar dimension reduction technique, it's not obvious where to find it. I do know that RapidMiner has an R Extension, which of course let's you access R inside RapidMiner.R has plenty of PCA libraries (Packages). The ones i mention below are all available on CRAN, which means any of the PCA Packages there satisfy the minimum Package requirements for documentation and vignettes (code examples). I can recommend pcaPP (Robust PCA by Projection Pursuit).
In addition, i can recommend two excellent step-by-step tutorials on PCA. The first is from the NIST Engineering Statistics Handbook. The second is a tutorial for Independent Component Analysis (ICA) rather than PCA, but i mentioned it here because it's an excellent tutorial and the two techniques are used for the similar purposes.
I'd like to know what method is best suited for predicting event occurrences.
For example, given a set of data from 5 years of malaria infection occurrences and several other factors that affect the occurrences, I'd like to predict the next five years for malaria infection occurrences.
What I thought of doing was to derive a kind of occurrence factor using fuzzy logic rules, and then average the occurrences with the occurrence factor to get the first predicted occurrence, and then average all again with the predicted occurrence and keep on iterating for all five years, but I decided to seek for help online.
There are many ways to do forecasting, each has its own advantages and disadvantages. The science of determining the accuracy of a forecast often consists of trying to minimize error. All forecasting comes down to using the past as a predictor of the future, adjusting it by some amount. E.g. tomorrow the temperature will be the same as today, plus or minus some amount. How you decide the +/- is what varies.
Here are a range of techniques you might want to review:
Moving Averages (simple, single, double)
Exponential Smoothing
Decomposition(Trend + Seasonality + Cyclicals + Irregualrities)
Linear Regression
Multiple Regression
Box-Jenkis (a.k.a. ARIMA,
Auto-Regressive Integrated Moving
Average)
Sorry, for the vague answer but forecasting is complex stuff.
What you describe about feeding your predictions back into the model to produce future predictions is standard stuff. I don't know if "fuzzy logic" gets you anything in particular. As any forecasting instructor will tell you, sometimes you just squint and look at the data. Context is everything.
I would use a logit or probit model to predict occurrence given a set of exogenous circumstances. Not sure why you want to iterate. That would basically be equivalent to including a lag in the regression formula. You could do it, and as long as the coefficient was <1, you wouldn't have the explosion problem.
If you want to introduce an element of endogeneity to the independent variables, you could use a VAR.
I think with your idea as stated, you'll have asymptotic behavior as time goes by. Either your data will converge to 0, or it will explode. That said, you'd probably have to give some data and/or describe its properties before anyone can help you. This is basically a simulation, and the factors are everything when it comes to extrapolation.