STAT0023作业代做、Moodle留学生作业代做、代写R程序

STAT0023 STATISTICS FOR PRACTICAL COMPUTING —ASSESSMENT 2 (2018/19 SESSION) Your solutions should be your own work and are to be submitted electronically to thecourse Moodle page by 12 noon on TUESDAY, 23RD APRIL 2019. Ensure that you electronically ‘sign’ the plagiarism declaration on the Moodle pagewhen submitting your work. Late submission will incur a penalty unless there are extenuating circumstances (e.g.medical) supported by appropriate documentation and notified within one week of thedeadline above. Penalties, and the procedure in case of extenuating circumstances, areset out in the latest editions of the Statistical Science Department student handbookswhich are available from the departmental web pages. Failure to submit this in-course assessment will mean that your overall examinationmark is recorded as “non-complete”, i.e. you will not obtain a pass for the course. Submitted work that exceeds the specified word count will be penalized. The penaltiesare described in the detailed instructions below. Your solutions should be your own work. When uploading your scripts, you will berequired to electronically sign a statement confirming this, and that you have read theStatistical Science department’s guidelines on plagiarism and collusion (see below). Any plagiarism or collusion can lead to serious penalties for all students involved,and may also mean that your overall examination mark is recorded as non-complete.Guidelines as to what constitutes plagiarism may be found in the departmental studenthandbooks: the relevant extract is provided on the ‘In-course assessment 2’ tab on theSTAT0023 Moodle page. The Turn-It-In plagiarism detection system may be used toscan your submission for evidence of plagiarism and collusion. You will receive feedback on your work via Moodle, and you will receive a provisionalgrade. Grades are provisional until confirmed by the Statistics Examiners’ Meeting inJune 2019.Background and overviewAnemia is a condition in which the oxygen-carrying capacity of blood is reduced relativeto the body’s requirements. These requirements depend on factors including age, altitude,and pregnancy status. According to the World Health Organisation (WHO), “Anemia isthe world’s second leading cause of disability and thus one of the most serious global publichealth problems. Anemia affects over half of pre-school children and pregnant women indeveloping countries and at least 30-40% in industrialized countries” (see https://www.who.int/medical_devices/initiatives/anaemia_control/en/ — click the blue text tofollow the link).The oxygen-carrying capacity of blood itself is determined by the concentration of haemoglobin(https://www.webmd.com/a-to-z-guides/understanding-anemia-basics): if haemoglobinlevels are too low then the body will not get enough oxygen. There are many forms of anemia,although the most common is caused by iron deficiency. Women of childbearing ageare particularly susceptible to anemia, because of the blood loss from menstruation andincreased blood supply demands during pregnancy (see the URL just cited). In principle,iron deficiency can be controlled to some extent by diet: red meat is a good source of iron,for example. In developed countries, iron supplements are readily available; in less developedcountries however, many people may be unable to afford such supplements or may beunaware of their existence.In a study published in 20161, an attempt was made to identify social, demographic andeconomic factors associated with anemia among women between 15 and 49 years of age inAfghanistan. The study authors used data from the 2010 UNICEF Multiple Indicator ClusterSurvey (MICS) for Afghanistan: see http://mics.unicef.org/ for general informationabout the MICS surveys, and http://cso.gov.af/Content/files/AMICS.pdf for a reportdescribing the 2010 survey for Afghanistan. The latter report can also be downloaded fromthe ‘In-course assessment 2’ tab of the STAT0023 Moodle page.The main points to note about the 2010 MICS survey for Afghanistan are as follows: The survey is designed to be nationally representative, with 13 314 households visitedover eight regions of the country. Responses were obtained from 98.5% of these households,in which 22 053 women were identified between the ages of 15 and 49. Interviewswere carried out with 21 290 of these women. Most of the interview questions are related to the social, economic and demographiccharacteristics of households and individual women: the questions are given in AppendixF of the Afghan survey report (see link above). Additionally, haemoglobintests were administered to women in half of the households. Haemoglobin levels (ing/Dl) are available for 9 199 women in the survey.The authors of the 2016 anemia study used the MICS survey data for the 9 199 women withhaemoglobin measurements. They discarded cases with haemoglobin levels above 24g/Dl asbeing unrealistic and therefore probably erroneous: this left 9 174 women in the data setused for further analysis. Each woman was classified as being anaemic or not, dependingon whether her altitude-adjusted haemoglobin level was below or above a critical threshold:the thresholds were obtained from WHO guidelines (11g/Dl for pregnant women, 12g/Dlfor others). The altitude adjustment aimed to provide an ‘equivalent haemoglobin level’in terms of blood oxygen capacity, taking into account the fact that oxygen saturation inblood reduces at high altitudes (see https://en.wikipedia.org/wiki/Effects_of_high_altitude_on_humans): the adjustment was based on the altitude of the province in whicheach woman lived. The authors then used logistic regression to model the dependence ofanemia status on selected covariates from the survey data. They carried out some furtheranalyses as well, but we don’t need to consider these.From the 2016 anemia study, three features of the authors’ analysis are worth noting:1Citation: Flores-Martinez A, Zanello G, Shankar B, Poole N (2016). Reducing Anemia Prevalence inAfghanistan: Socioeconomic Correlates and the Particular Role of Agricultural Assets. PLoS ONE 11(6):e0156878. doi:10.1371/journal.pone.0156878. A copy of this paper can also be downloaded from the ‘Incourseassessment 2’ tab of the STAT0023 Moodle page.1 The altitude-based adjustments to the haemoglobin measurements are imperfect, fortwo reasons. The first is that it’s hard to find any clear justification anywhere forthese particular adjustments (the study authors used the adjustments recommendedin a 2008 paper,2 but this doesn’t explain how they were derived — nor does it giveany indication of how accurate they are). The second is that the precise altitudes atwhich each woman lived are not known: they have been approximated by the altitudeof the provincial capital, which may be very inaccurate in mountainous areas. The authors pre-selected a group of potential covariates and included them all intheir model, without attempting to further refine the analysis e.g. by dropping nonsignificantcovariates or investigating potential interactions. There were many instances of multiple women living in the same household. There islikely to be an association between the anemia status of people in the same household,for example due to shared diets — and it is unlikely that this association can beexplained entirely using the covariate information available in the survey. This meansthat the responses are probably not independent given the covariates. In turn, thestandard errors, p-values and so forth in the study may be incorrect.The data used in the 2016 study have kindly been provided to me by one of its authors: ProfBhavani Shankar at the School of Oriental and African Studies. Moreover, we have permissionfrom UNICEF to use the data for this assessment. Therefore: on the ‘In-course assessment2’ tab of the STAT0023 Moodle page, you will find a CSV file called AnemiaData.csvwhich contains a modified version of the data used by the authors of the 2016 study. In thisdataset, one woman has been randomly sampled from each household so that there is noremaining within-household dependence. The file contains 5 421 records (i.e. rows of data):each record represents one woman. Haemoglobin measurements (in g/Dl) are provided forthe first 4 382 women, along with other information about the women and their households:full details can be found in the Appendix to these instructions. For the remaining 1 039women, however, the haemoglobin measurements are not provided: they are given as ‘1’.Your task in this assessment is to carry out some data preprocessing and then to use thedata from the first 4 382 records, to build a statistical model that will help you to: Understand the social, demographic and economic factors associated with variation inhaemoglobin levels between Afghan women in the 15-49 age range; and Estimate the haemoglobin levels for each of the 1 039 records where you don’t havethis information.Detailed instructionsYou may use either R or SAS for this assessment.2Citation: Sullivan, K. M., Mei, Z., Grummer-Strawn, L. and Parvanta, I. (2008). Haemoglobin adjustmentsto define anemia. Tropical Medicine & International Health, 13: 1267-1271. doi:10.1111/j.1365-3156.2008.02143.x21. Read the data into your chosen software package, and carry out any necessary recoding(e.g. to deal with the fact that ‘?1’ represents a missing value).2. Carry out an exploratory analysis that will help you to start building a sensible statisticalmodel to understand and predict each woman’s haemoglobin level. This analysisshould aim to identify an appropriate set of candidate variables to take into the subsequentmodelling exercise, as well as to identify any important features of the data thatmay have some implications for the modelling. You will need to consider the contextof the problem to guide your choice of exploratory analysis. See the ‘Hints’ below forsome ideas.3. Using your exploratory analysis as a starting point, develop a statistical model thatenables you to predict each woman’s haemoglobin level based on (a subset of) the othervariables in the dataset, and also to understand the variation of haemoglobin levelsbetween women. To be convincing, you will need to consider a range of models andto use an appropriate suite of diagnostics to assess them. Ultimately however, youare required to recommend a single model that is suitable for interpretation, and tojustify your recommendation. Your chosen model should be either a linear model, ageneralized linear model or a generalized additive model.4. Use your chosen model to predict the haemoglobin levels for each of the women wherethis information is missing, and also to estimate the standard deviation of your predictionerrors.Submission for this assessment is electronic, via the STAT0023 Moodle page. You are requiredto submit three files, as follows: A report on your analysis, not exceeding 2 500 words of text plus two pages of graphsand / or tables. The word count includes titles, footnotes, appendices, references etc.— in fact, it includes everything except the two pages of graphs / tables. Your reportshould be in three sections, as follows:I Describe briefly what aspects of the problem context you considered at the outset,how you used these to start your exploratory analysis, and what were theimportant points to emerge from this exploratory analysis.II Describe briefly (without too many technical details) what models you consideredin step (3) above, and why you chose the model that you did.III State your final model clearly, summarise what your model tells you about thefactors associated with variation of haemoglobin levels in Afghan women in the15–49 age range, and discuss any potential limitations of the model.Your report should not include any computer code. It should include some graphs and/ or tables, but only those that support your main points.Your report should be in PDF (recommended) or Word, and should be named as########_rpt.pdf or ########_rpt.docx as appropriate, where ######## is your3student ID number. For example, if your ID number is 150123456 and you are usingPDF, your script should be named 150123456_rpt.pdf. An R script or SAS program corresponding to your analysis and predictions. Yourscript /program should run without user intervention on any computer with R orSAS installed, providing the file AnemiaData.csv is present in the current workingdirectory / current folder. When run, it should produce any results that are mentionedin your report, together with the predictions and the associated standard deviations.The script / program should be named ########_ICA2.r or ########_ICA2.sas asappropriate, where ######## is your student ID number. You may not create anyadditional input files that can be referenced by your script: if you use R however, youmay use additional libraries if you wish (see ‘Hints’ below).A text file containing your predictions for the 1 039 women with missing haemoglobinmeasurements. This file should be named ########_pred.dat, where ######## is yourstudent ID number. The file should contain three columns, separated by spaces andwith no header. The first column should be the record identifier (corresponding to variableID in file AnemiaData.csv); the second should be the corresponding haemoglobinprediction, and the third should be the standard deviation of your prediction error.Marking criteriaThere are 75 marks for this exercise. These are broken down as follows:Report: 40 marks. The marks here are for: displaying awareness of the context for theproblem and using this to inform the statistical analysis; good judgement in the choiceof exploratory analysis and in the model-building process; a clear and well-justifiedargument; clear conclusions that are supported by the analysis; and appropriate choiceand presentation of graphs and / or tables. The mark breakdown is as follows:Awareness of context: 5 marks.Exploratory analysis: 10 marks. These marks are for (a) tackling the problem ina sensible way that is justified by the context (b) carrying out analyses that aredesigned to inform the subsequent modelling.Model-building: 10 marks. The marks are for (a) starting in a sensible place thatis justified from the exploratory analysis (b) appropriate use of model output anddiagnostics to identify potential areas for improvement (c) awareness of differentmodelling options and their advantages and disadvantages (d) consideration ofthe social, economic and demographic context during the model-building process.Quality of argument: 5 marks. The marks are for assembling a coherent ‘narrative’,for example by drawing together the results of the exploratory analysis soas to provide a clear starting point for model development, presenting the modelbuildingexercise in a structured and systematic way and, at each stage, linkingthe development to what has gone before.4Clarity and validity of conclusions: 5 marks. These marks are for stating clearlywhat you have learned about how and why haemoglobin levels vary betweenwomen, and for ensuring that this is supported by your analysis and modelling.Graphs and / or tables: 5 marks. Graphs and / or tables need to be relevant,clear and well presented (for example, with appropriate choices of symbols, linetypes, captions, axis labels and so forth). There is a one-slide guide to ‘Usinggraphics effectively’ in the slides / handouts for Lecture 1 of the course. Notethat you will only receive credit for any graphs in your report if your submittedscript / program generates and automatically saves these graphs, appropriatelylabelled, when it is run.Note that you will be penalised if your report exceeds EITHER the specified 2 500-wordlimit or the number of pages of graphs and / or tables. Following the UCL guidelines athttps: // www. ucl. ac. uk/ academic-manual/ chapters/ chapter-4-assessment-framework-taught-programmes/section-3-module-assessment# 3. 13 , the maximum penalty is 7 marks, and nopenalty will be imposed that takes the final mark below 30/75 if it was originally higher.Subject to these conditions, penalties are as follows: More than two pages of graphs and / or tables: zero marks for graphs and / ortables, in the marking scheme given above. Exceeding the word count by 10% or less: mark reduced by 4. Exceeding the word count by more than 10%: mark reduced by 7.In the event of disagreement between reported word counts on different software systems,the count used will be that from the examiner’s system. If you submit yourreport as a PDF file, the count will be obtained using an R function called PDFcount:this is available from the Moodle page in file PDFcount.r.Coding: 15 marks. There are 3 marks here for reading the data, preprocessing and handlingmissing values correctly and efficiently; 7 marks for effective use of your chosensoftware in the exploratory analysis and modelling (e.g. programming efficiently andcorrectly); and 5 marks for clarity of your code — commenting, layout, choice of variable/ object names and so forth.Prediction quality: 20 marks. The remaining 20 marks are for the quality of your predictions.Note, however, that you will only receive credit for your predictions if yoursubmitted ########_pred.dat file is identical to that produced by your script / programwhen it is run: if this is not the case, your predictions will earn zero marks.For these marks, you are competing against each other. Your predictions will be assessedusing the following score:�is the actual haemoglobin measurement (which I know) for the ith prediction;μi = E (Yi) is your corresponding prediction;σiis your quoted standard deviation for the prediction error.The score S is an approximate version of a proper scoring rule, which is designed toreward predictions that are close to the actual observation and are also accompanied byan accurate assessment of uncertainty (this was discussed during the Week 10 lecture,along with the rationale for using this score for the assessment). Low values are better.The scores of all of the students in the class (and the lecturer) will be compared:students with the lowest scores will receive all 20 marks, whereas those with the highestscores will receive fewer marks. The precise allocation of marks will depend on thedistribution of scores in the class.If you don’t supply standard deviations for your prediction errors, the values of the{σi} will be taken as zero: this means that your score will be ?∞ if you predict everyvalue perfectly (this is the smallest possible score, so you’ll get 20 marks in this case),and +∞ otherwise (this will earn you zero marks).STAT0023 Assessment 2 — Hints1. There is not a single ‘right’ answer to this assignment. There is a huge range of optionsavailable to you, and many of them will be sensible.2. You are being assessed not only on your computing skills, but also on your ability tocarry out an informed statistical analysis: material from other statistics courses (inparticular STAT0006/2002, for students who have taken it) will be relevant here. Toearn high marks, you need to take a structured and critical approach to the analysisand to demonstrate appropriate judgement in your choice of material to present.3. At first sight, the task will appear challenging. However, there is a lot of informationthat can guide you: look at some of the web links earlier in these instructions, and atother commentaries on anemia as a disease, to gain some understanding of what kindsof relationships you might look for in the data.4. When building your model, you have two main decisions to make. The first is: shouldit be a linear, generalized linear or generalized additive model? The second is: whichcovariates should you include? You might consider the following points:Linear, generalized linear or generalized additive? This is best broken down intotwo further questions, as follows: Conditional on the covariates, can the response variable be assumed to follow anormal distribution with constant variance? In this assignment, the responsevariable cannot be negative; nor can it exceed 24g/Dl (see above). Therefore,it cannot have exactly a normal distribution. However, you may find thatthe residuals from a linear regression model are approximately normal —6and you may judge that the approximation is adequate for your purposes.The ‘constant variance’ assumption may also be suspect: for positive-valuedquantities, it is common for the variability to increase with the mean. If thisis the case here, you need to decide whether it varies enough to matter: youneed to think about whether the effect is big enough that you can improveyour predictions (and hence your score!) by accounting for it e.g. usinga GLM. You might consider using your exploratory analysis to gain somepreliminary insights into this point. Are the covariate effects best represented parametrically or nonparametrically?Again, your exploratory analysis can be used to gain some preliminary insightsinto this. You may want to look at the material from week 6, forexamples of situations where a nonparametric approach is needed.Which covariates? The data file contains a lot of potential covariates, some of themfactors with several levels. You have many choices here, and you will need to takea structured approach to the problem in order to avoid running into difficulties.The following are some potentially useful ideas: Look at other literature on anemia and on the structure of Afghan society.What factors are considered to be the most important characteristicscontrolling haemoglobin levels? Are there known health inequalities withinAfghanistan? Can these be linked to covariates for which you have information?Obviously, if you do this then you will need to acknowledge yoursources in your report. Define useful summary measures on contextual grounds, and work with these.For example, many of the potential covariates are binary factors indicatingownership of different types of animals: you might decide to combine theseby summing them. Another covariate is ‘age’: you might decide to dividethis into three or so groups. Define new variables based on the correlations between the existing variables,and work with these. If several continuous variables are highly correlated, thenit is difficult to disentangle their effects and it may be preferable to work witha single ‘index’ that combines all of them. This is the basis of techniques suchas Principal Components Analysis, that were discussed during the Week 10lecture (along with how to implement them in R and SAS).You should not start to build any models until you have formed a fairly clearstrategy for how to proceed. Your decisions should be guided by your exploratoryanalysis, as well as your understanding of the context.5. Don’t forget to look for interactions! For example, one of the variables in the dataset is Sheep, which is a factor (i.e. categorical covariate) indicating whether or notthe woman’s household owns sheep: the authors of the 2016 study concluded that thisvariable was significantly associated with a woman’s anemia status. Another variable isWealthScore, which is an aggregate index of household wealth. It is conceivable thatsheep ownership is important for lower-income families where home-produced foodmay contribute a substantial proportion to the diet, but that it is less important for7wealthier families who can afford to buy food from elsewhere. Look at the analysis ofthe iris data from Workshop 2, for a similar kind of situation.6. You probably won’t find a perfect model in which all the assumptions are satisfied:models are just models. Moreover, you should not necessarily expect that your modelwill have much predictive power: it may be that the covariates in the data set justdon’t provide very much useful information about a woman’s haemoglobin levels. Youshould focus on finding the best model that you can, therefore — and acknowledge anydeficiencies in your discussion.7. If you use R for this assignment, you may load additional libraries if you wish. Youshould only do this, however, if you really understand what they are doing: overall,it is strongly recommended that you keep things fairly simple. See the feedback fromlast year’s assignment (available from the Moodle page) for more on this.8. If you use a linear model, it is straightforward to obtain the standard deviations ofyour prediction errors using either R or SAS (look at the material in Workshops 2 and 9respectively, to find out how to do it). However, for generalized linear and generalizedadditive models you need some additional computations. Specifically:(a) Suppose μi = E? (Yi) is your ith predicted haemoglobin level and that Yiis thecorresponding actual value.(b) Then your prediction error will be Yi μi.(c) Yi and μi are independent, because μiis computed using only information fromthe first 4 382 records and Yi relates to one of the ‘new’ records.(d) The variance of your prediction error is thus equal to Var (Yi) + Var (?μi).(e) You can calculate the standard error of ?μiin both R and SAS, when makingpredictions for new observations — see Workshops 6 and 9. Squaring this standarderror gives you Var (?μi).(f) You can estimate Var (Yi) by plugging in the appropriate formula for your chosendistribution — for example, if you’re using a gamma distribution (which is apossibility when using GLMs for non-negative response variables) then Var ( ?, where φ is the estimated dispersion parameter for your model (see Section2.1 of the notes for Workshop 6).(g) Hence you can estimate the standard deviation of your prediction error asVar ( Yi) + Var (μi).8Appendix: the AnemiaData.csv data setData sources and processingThe data provided in AnemiaData.csv are ultimately derived from the full 2010 AfghanistanMICS dataset, available from http://mics.unicef.org/surveys. The authors of the 2016study selected a subset of the variables from this survey as described in their supportinginformation (click the blue text to follow the link). These authors’ data have subsequentlybeen processed in the following way to create AnemiaData.csv:1. The variable names were modified for ease of interpretation.2. One women was randomly sampled from each household, so that the resulting data setdoes not contain any within-household dependence.3. The original dataset contained many dummy variables representing different levels ofthe same factor: for example, there were binary variables representing each of theeight regions of Afghanistan. Each group of dummy variables has been aggregatedinto a single factor variable with multiple levels: for example, the eight binary regionalvariables have been aggregated into a single factor Region with eight levels.4. Some less relevant variables, variables with large quantities of missing data, and variablesthat could be calculated from other information in the data set, were removed.An example of a ‘less relevant’ variable is the survey weight given to a particularwoman: this would be useful if we wanted to estimate (say) the mean haemoglobinlevel for all women in Afghanistan, but it is not needed here. A variable with largequantities of missing data is the mean upper-arm circumference (MUAC), which wasnot measured for any pregnant woman. Variables that could be calculated from otherinformation include ‘wealth quintiles’: these can be calculated from the WealthScorevariable.5. The Province variable, originally provided as a numeric code, was relabelled with theactual province names.6. The rows of the dataset were randomly shuffled: this is just to make it harder toidentify the rows on the basis of information that may be available on the internet.7. A sample of roughly 80% of the records was selected for use in the ‘model building’ partof the assessment (this will be referred to as ‘Group 1’ below), with the remaining 20%used for ‘prediction’ (‘Group 2’). This was done in such a way that the two sampleswere non-overlapping but had very similar distributions of all potential covariates.Specifically:(a) For each combination of the Province and Pregnant variables (see Appendix),80% of the women were sampled at random, without replacement, as candidatesto use in Group 1; and the remaining 20% were allocated to Group 2.9(b) For each of the numeric covariates in the data set, a Kolmogorov-Smirnov test wasperformed to test the null hypothesis that the underlying distributions in Groups1 and 2 are the same.(c) For each of the categorical covariates in the data set, a chi-squared test wasperformed to test the null hypothesis that the category proportions in Groups 1and 2 are the same.(d) The samples were accepted only if the p-values for all of the Kolmogorov-Smirnovand chi-squared tests were greater than 0.01. Otherwise, a new candidate samplewas drawn in step (a) and the procedure was repeated.The Kolmogorov-Smirnov and chi-squared tests are used here as a convenient wayto measure whether two distributions are roughly similar. Note, however, that thehaemoglobin levels were not included in this balancing exercise: this is because theperformance of predictions would be artificially enhanced if they were included (forexample, we would know that the mean haemoglobin level for Group 2 is similar tothat for Group 1). Note also that no attempt has been made to balance the groups interms of combinations of the covariates.8. The ‘Group 2’ records were placed at the end of the data table, with their haemoglobinlevels set to ?1; and a new ID variable was created so that each record has an ID numberbetween 1 and 5 421.Description of variablesThis section gives a brief description of each of the variables in AnemiaData.csv.Variable name DescriptionID Record ID, from 1 to 5 421Haemoglobin Individual’s haemoglobin level (g/Dl)Age Individual’s age (years)RecentBirth Has the individual given birth in the last two years? This takesone of two values: Yes and No.HHSize Number of household members.HHUnder5s Number of children under the age of 5 in the household.CleanWaterDoes the household have access either to water from a protectedsource (including a borehole), or to treated drinking water? (Yes/ No)TreatedWater Is the household’s water treated for drinking? (Yes / No)Electricity Does the household have electricity? (Yes / No)Continued on next page . . .10. . . continued from previous pageVariable name DescriptionToiletDoes the household have toilet facilities (flushing toilet, pit latrine,composting toilet, bucket, vault or sanitation)? (Yes /No)BikeScootCarWhat proportion of the following does the household own: (a)bike (b) scooter / motorcycle (c) car / truck (recorded as a valueof 0, 1/3, 2/3 or 1).AnimCart Does any household member own an animal-drawn cart? (Yes /No)AgricLandOwn Does any household member own agricultural land? (Yes / No)Cows Does the household own any cattle? (Yes / No)Horses Does the household own any horses, donkeys or mules? (Yes /No)Goats Does the household own any goats? 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